# On the Non-Commuting Graph of the Group $U_{6n}$

Sanhan Khasraw1, C.H. Jaf2, Nor Haniza Sarmin3, Ibrahim Gambo3
1 Department of Mathematics, College of Basic Education,
Salahadddin University-Erbil, Erbil, Iraq.
<EMAIL_ADDRESS>
2 Independent Researcher.
<EMAIL_ADDRESS>
3 Department of Mathematical Sciences, Faculty of Science,
Universiti Teknologi, Malaysia, 81310 UTM Johor Bahru, Malaysia.
<EMAIL_ADDRESS><EMAIL_ADDRESS>

###### Abstract

A non-commuting graph of a finite group $G$ is a graph whose vertices are non-
central elements of $G$ and two vertices are adjacent if they don’t commute in
$G$. In this paper, we study the non-commuting graph of the group $U_{6n}$ and
explore some of its properties including the independent number, clique and
chromatic numbers. Also, the general formula of the resolving polynomial of
the non-commuting graph of the group $U_{6n}$ are provided. Furthermore, we
find the detour index, eccentric connectivity, total eccentricity and
independent polynomials of the graph.

Keywords: Non-commuting graph, independent number, chromatic number, clique
number, resolving polynomial of a graph.

##  1 Introduction

In the last three decades, the interrelation of the structure in graphs and
algebra has provided us some interesting results and the topic has earned
significant attention from the research community, for example see [3, 8].

Suppose that $G$ is a finite group. We denote the center of $G$ by $Z(G)$ and
the centralizer of an element $a$ in $G$ by $C_{G}(a)$. If $C_{G}(a)$ is
abelian for every $a\in G$, then $G$ is said to be an AC-group [8]. The non-
commuting graph $\Gamma(G)$ of $G$ has $G-Z(G)$ as its vertex set in which two
vertices are adjacent if they don’t commute in $G$. The Hungarian
mathematician Paul Erdos was the first to introduce the concept of non-
commuting graph of a group in the 20th century. Since then, the topic has been
widely studied by researchers in the field, see [1, 9, 11]. It is worth-noting
that if the underlying group is abelian then the non-commuting graph has no
element since in that case $G=Z(G)$. In this paper we assume $G$ to be the
non-abelian group $U_{6n}$, which will be defined later. As a matter of fact
there are some researches studying commuting graph of a group, for instance
[2], and there are several articles about the non-commuting graph of a group,
for example, Abdollahi et al. [1] investigated on the non-commuting graph of
finite groups whereas Talebi [7] has conducted the same investigation for the
dihedral groups.

Most recently, Khasraw et al. [6] investigated the detour index, eccentric
connectivity, total eccentricity polynomials and the mean distance of the non-
commuting graph of dihedral group.

Some fundamental concepts that are related to this research throughout this
paper are provided in what follows. The graphs considered in this paper are
simple, that is, undirected with no loops or multiple edges, and a graph is
finite if both its vertex and edge sets are finite. Hence, we denote the
vertex and edge sets of the graph $\Gamma$ respectively by $V(\Gamma)$ and
$E(\Gamma)$ while we denote the number of vertices in the graph $\Gamma$ by
$n(\Gamma)$ and the number of its edges by $|E(\Gamma)|$.

Let $k\geq 2$. A sequence of $k$ vertices in which each vertex in the sequence
is adjacent to a vertex next to it is known as a path of a graph, denoted by
$P_{k}$. A path that does not repeat vertices is called a simple path. A path
that starts and ends at the same vertex is referred to us circuit while any
circuit that does not repeat vertices is a cycle, denoted as $C_{n}$, where
$n\geq 3$ [3, 4]. A graph is said to be connected if for every pair of
vertices $u$ and $v$, there is a path from $u$ to $v$, while a disconnected
graph consists of connected pieces called components. If vertices $u$ and $v$
are connected in $\Gamma$, the distance(detour distance) between $u$ and $v$,
denoted by $d(u,v)(D(u,v))$, is the length of a shortest(longest) $u-v$ path
in $\Gamma$. For a given vertex $v$ in $\Gamma$, the maximum distance between
$v$ and any other vertex in $\Gamma$ is called the eccentricity of $v$,
denoted by $ecc(v)$. The degree $\deg(v)$ of a vertex $v$ is the number of
edges incident with $v$ [3].

For a graph $\Gamma$, the polynomials $D(\Gamma,x)=\sum_{u,v\in
V(\Gamma)}x^{D(u,v)}$ [12], $\Xi(\Gamma,x)=\sum_{u\in
V(\Gamma)}deg_{\Gamma}(u)x^{ecc(u)}$ and $\Theta(\Gamma,x)=\sum_{u\in
V(\Gamma)}x^{ecc(u)}$ [13] are called the detour index, eccentric connectivity
and total eccentricity polynomials , respectively. The first derivative of
$D(\Gamma,x)$ at $1$ is called the detour index of the graph $\Gamma$, and is
denoted by $dd(\Gamma)$.

A graph is called regular if all of its vertices have the same degree and a
graph is called an $n-$regular if all of its vertices have degree $n$ [3].
While the chromatic number of a graph $\Gamma$, denoted by $\chi(\Gamma)$, is
the minimum number $c$ for which is $c-$vertex colorable [5]. The clique
number of a graph $\Gamma$, denoted by $\omega(\Gamma)$, is the size of the
largest complete subgraph of $\Gamma$. A vertex cover of a graph $\Gamma$ is a
subset $S$ of $V(\Gamma)$ such that every edge of $\Gamma$ has at least one
vertex in $S$. The minimum size of a vertex cover is denoted by $\tau(\Gamma)$
[10]. A non-empty set $S$ of $V(\Gamma)$ is called independent if no two
elements of $S$ are adjacent in $\Gamma$. The independent number is the
cardinality of a maximum independent set of a graph $\Gamma$ and is denoted by
$\alpha(\Gamma)$ [3]. Let $\Gamma$ be a graph. The independent polynomial was
defined in [16] as follows:
$I(\Gamma,x)=\sum_{i=0}^{\alpha(\Gamma)}s_{i}x^{i}$; where $s_{i}$ is the
number of independent sets of $\Gamma$ of cardinality $i$. While, in [17], the
vertex-cover polynomial is defined as
$\psi(\Gamma,x)=\sum_{i=0}^{n(\Gamma)}c_{i}x^{i}$; where $c_{i}$ is the number
of vertex covers of $\Gamma$ of cardinality $i$.

For an integer $k\geq 2$, a graph $\Gamma$ is called $k-$partite if
$V(\Gamma)$ accept a partition into $k$ classes such that every edge has its
ends in different classes, and vertices in the same partition class must not
be adjacent. If every two vertices from different partition classes are
adjacent, then the graph is called complete $k-$bipartite graph, denoted by
$K_{r_{1},r_{2},\cdots,r_{k}}$.

Let $\Gamma$ be a graph. Suppose $W=\\{w_{1},w_{2},\cdots,w_{k}\\}$ is a
subset of $V(\Gamma)$. The representation of a vertex $v$ of $\Gamma$ is the
$k$-vector $r(v|W)=(d(v,w_{1}),d(v,w_{2}),\cdots,d(v,w_{k}))$. If every pair
of distinct vertices of $\Gamma$ have distinct representations with respect to
$W$, then $W$ is called a resolving set for $\Gamma$. The cardinality of a
minimum resolving set for $\Gamma$ is called the metric dimension of $\Gamma$,
denoted by $\beta(\Gamma)$ [18]. The resolving polynomial of a graph $\Gamma$,
denoted by $\beta(\Gamma,x)$, is defined by
$\beta(\Gamma,x)=\sum_{i=\beta(\Gamma)}^{n(\Gamma)}r_{i}x^{i}$, where $r_{i}$
is the number of resolving sets for $\Gamma$ of cardinality $i$. The sequence
$(r_{\beta(\Gamma)},r_{\beta(\Gamma)+1},\cdots,r_{n{\Gamma}})$ is called the
resolving sequence. The set of all distinct roots of $\beta(\Gamma,x)$ is
denoted by $Z(\beta(\Gamma,x))$.

The group $U_{6n}$, of order $6n$, is defined by

$U_{6n}=\langle a,b\;|\;a^{2n}=b^{3}=1,a^{-1}ba=b^{-1}\rangle$

for $n\geq 1$ with center $Z(U_{6n})=\langle a^{2}\rangle$ [14]. Throughout
this paper, the elements of $U_{6n}-Z(U_{6n})$ are partitioned into four
disjoint sets according to centralizers of elements, see Lemma 2.1, as
follows: $\Omega_{1}=\\{a^{2r+1}\,:\,0\leq r\leq n-1\\}$,
$\Omega_{2}=\\{a^{2r+1}b\,:\,0\leq r\leq n-1\\}$,
$\Omega_{3}=\\{a^{2r+1}b^{2}\,:\,0\leq r\leq n-1\\}$, and
$\Omega_{4}=\\{a^{2r}b^{k}\,:\,0\leq r\leq n-1,\,k=1,2\\}$. It is clear that
$|\Omega_{1}|=|\Omega_{2}|=|\Omega_{3}|=n$, and $|\Omega_{4}|=2n$.

This paper consists of four sections. In the introduction section, some
necessary definitions and notations are presented. In Section 2, some
properties of the non-commuting graph $\Gamma({U_{6n}})$ of the group $U_{6n}$
are studied. In Section 3, we find the general formula of the resolving
polynomial of the non-commuting graph of the group $U_{6n}$. In Section 4, we
find the detour index, eccentric connectivity, total eccentricity and
independent polynomials of the non-commuting graph $\Gamma({U_{6n}})$.

##  2 Some basic properties of the non-commuting graph $\Gamma(U_{6n})$

This section contains some lemmas on non-commuting graph that are used to
obtain some important results that follow.

We begin with the following lemma, which can be found in [8].

######  Lemma 2.1.

For the group $U_{6n}$, and $0\leq r\leq n-1$, we have the following

  1. 1.

$Z(U_{6n})=\langle a^{2}\rangle$,

  2. 2.

$C_{U_{6n}}(a^{2r+1})=\langle a\rangle,$

  3. 3.

$C_{U_{6n}}(a^{2r+1}b)=\langle a^{2}\rangle\cdot\langle\\{a^{2s+1}b:0\leq
s\leq n-1\\}\rangle$,

  4. 4.

$C_{U_{6n}}(a^{2r+1}b^{2})=\langle
a^{2}\rangle\cdot\langle\\{a^{2s+1}b^{2}:0\leq s\leq n-1\\}\rangle$,

  5. 5.

$C_{U_{6n}}(a^{2r}b)=\langle
a^{2}\rangle\cdot\langle\\{a^{2s}b,a^{2s}b^{2}:0\leq s\leq n-1\\}\rangle$.

The following useful lemma is used in calculating the degree of vertices in
$\Gamma({U_{6n}})$, which can be found in [1].

######  Lemma 2.2.

Let $G$ be a non-abelian finite group and let $x$ be a vertex of $\Gamma(G)$.
Then $\deg(x)=|G|-|C_{G}(x)|$, where $C_{G}(x)$ is the centralizer of the
element $x$ in $G$.

The above lemmas lead to the following

######  Corollary 2.3.

Let $n\geq 1$ be an integer and let $\Gamma=\Gamma({U_{6n}})$. Then, for
$0\leq r\leq n-1$ and $k=1,2$, we have

  1. 1.

$\deg_{\Gamma}(a^{2r+1})=4n,$

  2. 2.

$\deg_{\Gamma}(a^{2r+1}b^{k})=4n,$

  3. 3.

$\deg_{\Gamma}(a^{2r}b^{k})=3n.$

######  Theorem 2.4.

For $n\geq 1,$ $\Gamma=\Gamma({U_{6n}})$, the number of edges of the graph
$\Gamma$ is $|E(\Gamma)|=9n^{2}$.

###### Proof.

From Corollary 2.3, we have
$|E(\Gamma)|=\frac{1}{2}\sum_{x\in\Gamma}\deg(x)=\frac{1}{2}\left(12n^{2}+6n^{2}\right)=9n^{2}$.
∎

######  Theorem 2.5.

For $n\geq 1$, let $\Gamma=\Gamma({U_{6n}})$ and $\Omega$ is a subset of
$U_{6n}$. Then $\Gamma=K_{n,n,n,2n}$ if and only if
$\Omega=\Omega_{1}\cup\Omega_{2}\cup\Omega_{3}\cup\Omega_{4}$.

###### Proof.

Assume $\Omega=\Omega_{1}\cup\Omega_{2}\cup\Omega_{3}\cup\Omega_{4}$. Then
$C_{\Omega}(a^{2r+1})=\Omega_{1},C_{\Omega}(a^{2r+1}b)=\Omega_{2},C_{\Omega}(a^{2r+1}b^{2})=\Omega_{3}$
and $C_{\Omega}(a^{2r}b^{k})=\Omega_{4}$ for $k=1,2$, so
$\Gamma=K_{n,n,n,2n}$. Conversely, assume $\Gamma=K_{n,n,n,2n}$, then by
Corollary 2.3, $\Omega=\Omega_{1}\cup\Omega_{2}\cup\Omega_{3}\cup\Omega_{4}$.
∎

In [3], the relation between the independent number and the vertex cover with
number of vertices has been given as in the following lemma.

######  Lemma 2.6.

Let $\Gamma$ be a graph. Then $\alpha(\Gamma)+\tau(\Gamma)=n(\Gamma)$.

######  Theorem 2.7.

For the graph $\Gamma=\Gamma({U_{6n}})$, $\alpha(\Gamma)=2n$.

###### Proof.

From Lemma 2.1 and Theorem 2.5, one can see that $\Omega_{4}$ is the largest
part of the 4-partite graph $K_{n,n,n,2n}$. Thus, $\alpha(\Gamma)=2n.$ ∎

######  Corollary 2.8.

For the graph $\Gamma=\Gamma({U_{6n}})$, $\tau(\Gamma)=3n$.

###### Proof.

The result follows from Lemma 2.6 and Theorem 2.7. ∎

######  Theorem 2.9.

For the graph $\Gamma=\Gamma({U_{6n}})$, we have
$\chi(\Gamma)=\omega(\Gamma)=4.$

###### Proof.

By Theorem 2.5, the clique of $\Gamma$ can only contain one vertex from each
$\Omega_{i}(i=1,...,4)$. Therefore, $\omega(\Gamma)=4$. Since the group
$U_{6n}$ is an AC-group, then $\chi(\Gamma)=\omega(\Gamma)$. ∎

######  Theorem 2.10.

Let $\Gamma=\Gamma({U_{6n}})$, and
$\Omega=\Omega_{1}\cup\Omega_{2}\cup\Omega_{3}\cup\Omega_{4}$. There exist no
subset $S$ of $\Omega$ such that $\Gamma=C_{5}$.

###### Proof.

Suppose that $\Gamma=C_{5}$. Then at least two vertices, say $v_{1}$ and
$v_{2}$, on $\Gamma$ belong to some $\Omega_{i}$ for $i\in\\{1,2,3,4\\}$.
There are three cases to consider. Case 1. If the other three vertices belong
to $\Omega_{j}$, $j\in\\{1,2,3,4\\}$ and $j\neq i$, then $\Gamma=K_{2,3}$,
which is contradiction. Case 2. If two of the other three vertices belong to
the same $\Omega_{j}$ and the third one belongs to $\Omega_{k}$, where $j\neq
i\neq k$, then $\Gamma=K_{2,2,1}$, which is also a contradiction. Case 3. If
each of the other three vertices belongs to a different $\Omega_{j}$,
$j\in\\{1,2,3,4\\}$ and $j\neq i$, then $\Gamma=K_{2,1,1,1}$, which is again a
contradiction. ∎

######  Theorem 2.11.

Let $\Gamma=\Gamma({U_{6n}})$, and $\Omega$ is a subset of $V(\Gamma)$. Then
$\Gamma\neq P_{k}$ for $k\geq 4$.

###### Proof.

For $k<4$, we show that, $\Gamma=P_{2}$ or $P_{3}$.
Case 1. $\Omega=\\{x,y\\}$ where $x\notin C_{U_{6n}}(y)$, then $\Gamma=P_{2}$.
Case 2. Let $\Omega=\\{x,y,z\\}$ where $x\notin C_{U_{6n}}(y)$. If $z\notin
C_{U_{6n}}(y)$ and $z\notin C_{U_{6n}}(y)$ then $\Gamma=C_{3}$. But if $z$ is
either in $C_{U_{6n}}(x)$ or $C_{U_{6n}}(y)$ then $\Gamma=P_{3}$.
If we add one more element, say $w$, to $\Omega$ then we have two
possibilities; either $w\notin C_{U_{6n}}(x)$ and $w\notin C_{U_{6n}}(y)$, and
this implies that there will be edges $d\sim x$ and $d\sim y$, which means
$\Gamma\neq P_{4}$, or $w$ is in the centralizer of one of them, in this case
say $w\in C_{U_{6n}}(x)$, implies that there will be an edge $d\sim y$, which
again means $\Gamma\neq P_{4}$. ∎

######  Theorem 2.12.

Let $\Gamma=\Gamma({U_{6n}})$, and $\Omega$ is a subset of $V(\Gamma)$. Then
$\Gamma$ is $2n-$regular if and only if
$\Omega=\Omega_{1}\cup\Omega_{2}\cup\Omega_{3}$.

###### Proof.

If the graph $\Gamma$ is $2n-$regular, then every vertex in $\Gamma$ has
degree $2n$. By Corollary 2.3,
$\Omega=\Omega_{1}\cup\Omega_{2}\cup\Omega_{3}$. Conversely, Let
$\Omega=\Omega_{1}\cup\Omega_{2}\cup\Omega_{3}$. By Corollary 2.3, $deg(u)=2n$
for all $u\in\Omega$. Thus, $\Gamma$ is a $2n-$regular graph. ∎

##  3 Resolving polynomial of the non-commuting graph $\Gamma(U_{6n})$

In this section, we find the metric dimension and resolving polynomial of the
non-commuting graph $\Gamma(U_{6n})$.

We start by the following useful lemma about resolving polynomial
$\beta(\Gamma,x)$ of a graph $\Gamma$ of order $n$.

######  Lemma 3.1.

If $\Gamma$ is a connected graph of order $n$, then it has only one resolving
set of cardinality $n$, which is $V(\Gamma)$, and $n$ resolving sets of
cardinality $n-1$.

######  Theorem 3.2.

Let $\Gamma=\Gamma(U_{6n})$ be a non-commuting graph on $U_{6n}$. Then
$\beta(\Gamma)=\left\\{\begin{tabular}[]{ll}$3$&\mbox{ if }$n=1$\\\
$5n-4$&\mbox{ if }$n>1$.\\\ \end{tabular}\right.$

###### Proof.

Case 1. When $n=1$. The graph $\Gamma$ is a split graph with 5 vertices such
that $V(\Gamma)=K\cup S$, where $K=\\{a,ab,ab^{2}\\}$ is the complete part and
$S=\\{b,b^{2}\\}$ is the independent part. The resolving set for $\Gamma$ of
minimal cardinality is $W=\\{a,ab,b\\}$.

Case 2. When $n>1$. Since every two distinct vertices $u$ and $v$ are non-
adjacent in $\Omega_{i}$, $i\in\\{1,2,3,4\\}$, then $\beta(\Gamma)\geq 5n-4$.
On the other hand, it is clear that the set $W=\\{a^{2r+1},$ $a^{2r+1}b,$
$a^{2r+1}b^{2},$ $a^{2r}b^{k};$ $k=1,2;\;$ $0\leq r\leq n-2\\}$ is the
resolving set for $\Gamma$ of cardinality $5n-4$. This implies that
$\beta(\Gamma)\leq 5n-4$ ∎

######  Theorem 3.3.

Let $\Gamma=\Gamma(U_{6n})$ be a non-commuting graph on $U_{6n}$. Then

$\beta(\Gamma,x)=\begin{cases}x^{3}(x+2)(x+3)&\mbox{ if }n=1,\\\
x^{5n-4}(x+n)^{3}(x+2n)&\mbox{ if }n>1.\end{cases}$

###### Proof.

There are two cases to consider. When $n=1$. By Theorem 3.2, it is required to
find the resolving sequence $(r_{3},r_{4},r_{5})$ of length 3. Since the graph
$\Gamma$ is a split graph with 5 vertices where its complete part consists of
3 vertices and the independent part consists of 2 vertices, then
$r_{3}={{2}\choose{1}}{{3}\choose{2}}=6$.
By Lemma 3.1, $r_{4}=5$ and $r_{5}=1$.
When $n>1$. By Theorem 2.5, the graph $\Gamma$ is 4-partite. By Theorem 3.2,
we need to find the resolving sequence
$(r_{5n-4},r_{5n-3},r_{5n-2},r_{5n-1},r_{5n})$ of length 5.
For $r_{5n-4}$: By Theorem 2.5 and by the multiplication principal,

$r_{5n-4}={{n}\choose{n-1}}{{n}\choose{n-1}}{{n}\choose{n-1}}{{2n}\choose{2n-1}}=2n^{4}.$

For $r_{5n-3}$: It is required to count all the resolving sets for $\Gamma$ of
cardinality $5n-3$. There are four cases, in the first case,
${{n}\choose{n}}{{n}\choose{n-1}}{{n}\choose{n-1}}{{2n}\choose{2n-1}}$; in the
second case,
${{n}\choose{n-1}}{{n}\choose{n}}{{n}\choose{n-1}}{{2n}\choose{2n-1}}$; in the
third case,
${{n}\choose{n-1}}{{n}\choose{n-1}}{{n}\choose{n}}{{2n}\choose{2n-1}}$; and in
the fourth case,
${{n}\choose{n-1}}{{n}\choose{n-1}}{{n}\choose{n-1}}{{2n}\choose{2n}}$
possible resolving sets of cardinality $5n-3$. By the addition principal,
$r_{5n-3}=7n^{3}$.

For $r_{5n-2}$: We need to count all the resolving sets for $\Gamma$ of
cardinality $5n-2$. Again, we have six cases to consider, in the first case,
${{n}\choose{n}}{{n}\choose{n}}{{n}\choose{n-1}}{{2n}\choose{2n-1}}$; in the
second case,
${{n}\choose{n}}{{n}\choose{n-1}}{{n}\choose{n}}{{2n}\choose{2n-1}}$; in the
third case,
${{n}\choose{n}}{{n}\choose{n-1}}{{n}\choose{n-1}}{{2n}\choose{2n}}$; in the
fourth case,
${{n}\choose{n-1}}{{n}\choose{n}}{{n}\choose{n}}{{2n}\choose{2n-1}}$; in the
fifth case, ${{n}\choose{n-1}}{{n}\choose{n}}{{n}\choose{n-1}}$
${{2n}\choose{2n}}$; and in the sixth case,
${{n}\choose{n-1}}{{n}\choose{n-1}}{{n}\choose{n}}{{2n}\choose{2n-1}}$;
possible resolving sets of cardinality $5n-2$. By the addition principal,
$r_{5n-2}=9n^{2}$. By Lemma 3.1, $r_{5n-1}=5n$ and $r_{5n}=1$. ∎

######  Corollary 3.4.

Let $\Gamma=\Gamma(U_{6n})$ be a non-commuting graph on $U_{6n}$. Then for
$n=1$, $Z(\beta(\Gamma,x))=\\{0,-2,-3\\}$, and for all $n>1$,
$Z(\beta(\Gamma,x))=\\{0,-n,-2n\\}$.

##  4 Some polynomials of the non-commuting graph $\Gamma(U_{6n})$

In this section some properties of non-commuting graphs of $U_{6n}$ are
explored, namely the detour index, the eccentric connectivity, the total
eccentricity and the independent polynomials.

######  Lemma 4.1.

Let $\Gamma({U_{6n}})$ be a non-commuting graph of $U_{6n}$. Then,
$D(u,v)=5n-1$ for any $u,v\in\Gamma({U_{6n}})$.

###### Proof.

From Theorem 2.5, one can see that no two vertices in $\Omega_{i}$ are
adjacent, and each vertex in $\Omega_{i}$ is adjacent to every vertex in
$\Omega_{j}$ for $i\neq j$ and $i,j\in\\{1,2,3,4\\}$. Then for all
$u,v\in\Omega$, where
$\Omega=\Omega_{1}\cup\Omega_{2}\cup\Omega_{3}\cup\Omega_{4}$, there is a
$u-v$ path of length $5n-1$. ∎

######  Theorem 4.2.

Let $\Gamma({U_{6n}})$ be a non-commuting graph of $U_{6n}$. Then,
$D(\Gamma({U_{6n}}),x)=\frac{5n(5n-1)}{2}x^{5n-1}$.

###### Proof.

We have that $|\Gamma({U_{6n}})|=5n$. Then there are
${{5n}\choose{2}}=\frac{5n(5n-1)}{2}$ possibilities of choosing distinct pairs
of vertices from $\Gamma({U_{6n}})$. By Lemma 4.1, $D(u,v)=5n-1$ for any
distinct pairs of $u,v\in\Gamma({U_{6n}})$. Thus,
$D(\Gamma({U_{6n}}),x)=\sum_{\\{u,v\\}}x^{D(u,v)}={{5n}\choose{2}}x^{5n-1}=\frac{5n(5n-1)}{2}x^{5n-1}$.
∎

Theorem 4.2 leads to the following result.

######  Corollary 4.3.

Let $\Gamma({U_{6n}})$ be a non-commuting graph of $U_{6n}$. Then,
$dd(\Gamma({U_{6n}}))=\frac{5n(5n-1)^{2}}{2}$.

######  Lemma 4.4.

Let $\Gamma({U_{6n}})$ be a non-commuting graph of $U_{6n}$. Then, $ecc(u)=2$
for every $u\in\Omega$, where
$\Omega=\Omega_{1}\cup\Omega_{2}\cup\Omega_{3}\cup\Omega_{4}$.

###### Proof.

In $\Omega_{i}$, there is no edge between any pair of distinct vertices, for
$i\in\\{1,2,3,4\\}$. Furthermore, each vertex in $\Omega_{i}$ is adjacent to
every vertex in $\Omega_{j}$, for $i\neq j$ and $i,j\in\\{1,2,3,4\\}$. Then
the maximum distance between any vertex in $\Omega_{i}$ and other vertices in
$\Omega$ is $2$. Therefore, $ecc(u)=2$, for every $u\in\Omega$. ∎

######  Theorem 4.5.

Let $\Gamma=\Gamma({U_{6n}})$ be a non-commuting graph of $U_{6n}$ and
$\Omega=\Omega_{1}\cup\Omega_{2}\cup\Omega_{3}\cup\Omega_{4}$. Then,

  1. 1.

$\Theta(\Gamma,x)=5nx^{2}$.

  2. 2.

$\Xi(\Gamma,x)=18n^{2}x^{2}$.

###### Proof.

Since the graph $\Gamma$ has $5n$ vertices, then

  1. 1.

By Lemma 4.4 $ecc(u)=2$, for every $u\in\Omega$, so
$\Theta(\Gamma,x)=\sum_{u\in V(\Gamma)}x^{ecc(u)}=5nx^{2}$.

  2. 2.

By Corollary 2.3, $3n$ vertices in $\Omega_{1}\cup\Omega_{2}\cup\Omega_{3}$
are of degree $4n$ and $2n$ vertices in $\Omega_{4}$ are of degree $3n$ and
from Lemma 4.4 we see that $\Xi(\Gamma,x)=\sum_{u\in
V(\Gamma)}deg_{\Gamma}(u)x^{ecc(u)}=(3n(4n)+2n(3n))x^{2}=18n^{2}x^{2}$.

∎

######  Theorem 4.6.

Let $\Gamma=\Gamma({U_{6n}})$ be a non-commuting graph of $U_{6n}$. Then the
independent polynomial is as follows,

$I(\Gamma;x)=1+\sum_{k=1}^{n}\left({{2n}\choose{k}}+3{{n}\choose{k}}\right)x^{k}+\sum_{k=n+1}^{2n}{{2n}\choose{k}}x^{k}.$

###### Proof.

By Theorem 2.7, the independent number of $\Gamma$, $\alpha(\Gamma)=2n$. Then
$I(\Gamma;x)=\sum_{k=0}^{2n}s_{k}x^{k}.$ It is easy to see that $s_{0}=1$
since the only independent set of cardinality zero is the empty set. Moreover,
we have three independent sets, $\Omega_{1},\Omega_{2}$ and $\Omega_{3}$, each
of cardinality $n$ and one independent set, $\Omega_{4}$, of cardinality $2n$.
Thus, there are $s_{k}=3{{n}\choose{k}}+{{2n}\choose{k}}$ possibilities of
independent sets of cardinality $k$ for $1\leq k\leq n$, and
$s_{k}={{2n}\choose{k}}$ possibilities of independent sets of cardinality $k$
for $n<k\leq 2n$. Then the result follows. ∎

######  Corollary 4.7.

Let $\Gamma=\Gamma({U_{6n}})$ be a non-commuting graph of $U_{6n}$. Then, the
vertex-cover polynomial is as follows,

$\psi(\Gamma;x)=x^{5n}+\sum_{k=1}^{n}\left({{2n}\choose{k}}+3{{n}\choose{k}}\right)x^{5n-k}+\sum_{k=n+1}^{2n}{{2n}\choose{k}}x^{5n-k}.$

###### Proof.

The result comes from Theorem 4.6 and the fact that
$\psi(\Gamma,x)=x^{n(\Gamma)}I(\Gamma,x^{-1})$ [15]. ∎

## Conclusion

In this paper, some properties of the non-commuting graph of the group
$U_{6n}$ is presented. The general formula of the resolving polynomial of the
non-commuting graph of the group $U_{6n}$ are provided. In the last section of
this paper, we also provided the detour index, eccentric connectivity, total
eccentricity and independent polynomials of non-commuting graphs on $U_{6n}$.

## Acknowledgment

The third author would like to appreciate Universiti Teknologi Malaysia for
the research grant with number 20H70 under Fundamental Research Grant scheme
and the fourth author would like to acknowledge his postdoctoral fellowship.

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# Task allocation interface design and personalization in gamified
participatory sensing for tourism

Shogo Kawanaka
Nara Institute Science and Technology
Takayama-cho 8916-5, Ikoma
Nara, Japan, 630-0192
<EMAIL_ADDRESS>
Juliana Miehle
Institute of Communications Engineering
Ulm University
Albert-Einstein-Allee 43, Ulm, Germany, 89081
Yuki Matsuda
Nara Institute Science and Technology / Riken AIP
Takayama-cho 8916-5, Ikoma
Nara, Japan, 630-0192
Hirohiko Suwa
Nara Institute Science and Technology / Riken AIP
Takayama-cho 8916-5, Ikoma
Nara, Japan, 630-0192
Keiichi Yasumoto
Nara Institute Science and Technology / Riken AIP
Takayama-cho 8916-5, Ikoma
Nara, Japan, 630-0192
Wolfgang Minker
Institute of Communications Engineering
Ulm University
Albert-Einstein-Allee 43, Ulm, Germany, 89081

###### Abstract

The collection of spatiotemporal tourism information is important in smart
tourism and user-generated contents are perceived as reliable information.
Participatory sensing is a useful method for collecting such data, and the
active contribution of users is an important aspect for continuous and
efficient data collection. This study has focused on the impact of task
allocation interface design and individual personality on data collection
efficiency and their contribution in gamified participatory sensing for
tourism. We have designed two types of interfaces: a map-based with active
selection and a chat-based with passive selection. Moreover, different levels
of elaborateness and indirectness have been introduced into the chat-based
interface. We have employed the Gamification User Types Hexad framework to
identify the differences in the contributions and interface preferences of
different user types. The results of our tourism experiment with 108
participants show that the map-based interface collects more data, while the
chat-based interface collects data for spots with higher information demand.
We also found that the contribution to sensing behavior and interface
preference differed depending on the individual user type.

_Keywords_ Smart Tourism $\cdot$ Participatory Sensing $\cdot$ Interface
Design $\cdot$ Communication Style $\cdot$ Personalization

##  1 Introduction

The tourism industry has become a major industry accounting for 10.3% of the
world’s total GDP in 2019, the demand is increasing every year, and services
are needed to provide more comfortable tourism for the expansion of the
industry in the future 111Economic Impact — World Travel and Tourism Council
(WTTC): https://wttc.org/Research/Economic-Impact (Accessed at 12, Feb.,
2021). Information on tourist destinations is very important when deciding on
a destination [13]. With the development and spread of information technology,
people can easily post and view their own tourism experiences, and the
information generated by consumers through their actual experiences is
accepted as a more effective and reliable source of information [30]. It is
also changing tourism style, and a new of tourism, such as on-site tourism,
which determines the next destination while sightseeing, is becoming popular
[6]. Research on on-site tourism planning that takes into account the
dynamically changing tourism context has been conducted, and the realization
of such systems will provide a highly satisfying tourism experience [12].
However, the realization of such systems requires dynamic tourism information
with high spatio-temporal resolution. In order to collect such information,
the participatory sensing approach [3], in which mobile devices owned by the
general public such as smartphones are used as sensing devices, will be
effective [8]. While it has the property of collecting data with high spatio-
temporal resolution at low cost, the problem is that the amount and quality of
collected data depends on the contribution of the participating users. As an
incentive mechanism for improving user contributions and motivation to
participate, gamification that incorporates game concepts and mechanisms into
content other than games is attracting attention [5]. Gamification has been
applied in a variety of fields and has been shown to be effective so far [33,
1]. According to literature on designing effective incentive mechanisms,
points, rankings/leaderboards, and achievement are often introduced as
gamification mechanics, and affect the user positively, particularly in
participatory sensing [14, 28, 24]. However, previous researches suggest that
empirical studies are required in order to clarify the effects of gamification
in each participatory sensing context or domain [10, 24, 29]. Additionally,
the importance of individually personalizing the gamification design and the
interface rather than the full package has also been revealed [9, 15].

In this paper, we investigate the effects of different task allocation
interfaces and gamification user types on tourism information collection
efficiency and tourism satisfaction in gamified participatory sensing for
tourism. We designed two types of task allocation interfaces, map-based and
chat-based, and implemented them on our gamified participatory sensing
platform application. We also designed four different communication style
sentences to investigate the appropriate way to ask the sensing tasks through
the chat with agent character. Furthermore, we employed the Gamification User
Types Hexad framework to elucidate how an individual’s personality influences
their contribution to sensing and interface preference. Then, we set these
four main research questions:

RQ1

How does the different task allocation interfaces affect the quantity and
quality of dynamic tourism information collection?

RQ2

Do the different task allocation interfaces have an impact on tourism
satisfaction of the tourists?

RQ3

Is there a relationship between tourism information collection efficiency and
interface preference and gamification user type?

RQ4

What is the impact of different communication style sentences in a chat-based
interface?

To elucidate these research questions, we conducted large scale experiment
with 108 participants at actual sightseeing attractions in Nara, Japan.

As a result, we found that there was no difference in the effect of each
interface on sightseeing satisfaction, but the characteristics of the
collected data that, map-based allows for the collection of quantitative data
and chat-based allows for the efficient collection of data needed by the
system, were different. In addition, we found that different user types had
different tendencies for their contribution to sensing and their interface
preferences. Moreover, 47 % of the participants noticed a difference in the
agent’s communication style, showing that a large number of participants were
aware of these subtle changes. Furthermore, the participants significantly
preferred the elaborate communication style over the concise one. However,
there is no preference for the indirectness dimension. This shows that there
is no general preference in the system’s communication style and therefore the
preference appears to be individual for every person.

The rest of this paper will describe the following. First, we describe related
work on the application of gamification in tourism and personalization in
gamification. Then, we present the design and implementation of our designed
two interfaces, and report the results of our experiments. Finally, we
summarize this paper based on the results obtained from each experiment.

##  2 Related Work

###  2.1 Gamification in Tourism

Gamification is often introduced in the tourism domain in order to raise brand
awareness, enhance tourist experiences, destination loyalty, consumer loyalty
and engagements so far [29, 34]. However, according to Xu et al. [34],
academic research on the application of gamification specifically in the
tourism field is still scarce. Cesário et al. [4] designed two mobile apps, AR
(Augmented Reality) game-based and story-based, to better understand teenage
museum tourism behavior and to inform the suitable museum mobile app design.
Their study also focused on user personalities and found that story-based
strategies are suitable for a broader set of personalities. There are a few
researches investigating the impact of gamification on dynamic tourism
information collection with various gamification mechanics. Although a
comprehensive evaluation using various mechanics was conducted, it is not
clear which gamification mechanism had an impact on which outcome [18]. The
prior work by Kawanaka et al. have previously investigated the impact of
different task load and reward mechanisms on data collection efficiency and
tourism behavior in a gamified participatory sensing application for tourism
[16]. However, there is room to investigate the elements needed to personalize
the design, such as the task allocation interfaces and user preferences.

###  2.2 Interface and Interaction Design

The notion that user interface design can be informed by other design
practices has a rich tradition in HCI. During the first boom of computer games
in the early 1980s, Malone wrote seminal papers deriving “heuristics for
designing enjoyable user interfaces” from video games [19]. One of the studies
on interface design in terms of data collection is the study of interfaces in
online surveys, which was reported by Kim et al. [17]. In this study, a web-
based interface and a chatbot-based interface were used .They used formal
style as basic style and casual style which is more friendly. The experimental
results suggested, the quality of the responses was higher for chatbots than
the web interface. Second, high quality answers were obtained in casual
conversational style only in chatbots. From these results, it is suggested
that differences in interface and conventional style in agent interaction
affects the quality of data. Another related study of communication styles is
elaborateness and indirectness which was proposed by Pragst et al. [26].
Elaborateness refers to the amount of additional information provided to the
user and indirectness describes how concretely the information that is to be
conveyed is addressed by the speaker. Miehle et al. [23] addressed the issues
of how varying communication styles of a spoken user interface are perceived
by users and whether there exist global preferences in the communication
styles elaborateness and indirectness. It is shown that the system’s
communication style influences the user’s satisfaction and the user’s
perception of the dialogue and that there is no general preference in the
system’s communication style. The authors conclude that spoken dialogue
systems need to adapt their communication style to each user individually
during every dialogue in order to achieve a high level of user satisfaction.
In [22], a classification approach is presented addressing the estimation of
the user’s communication style in a spoken dialogue. It is shown that it is
feasible to automatically detect the elaborateness and indirectness of the
user during a dialogue.

###  2.3 Personalization in Gamification

Several studies have explored the relations between gamification design and
user motivational factors or personalities in human-computer interaction
research area [11, 15]. Jia et al. [15] investigated the relationships among
individuals’ personality traits and perceived preferences for various
motivational affordances used in gamification. Their research showed
correlations between each of the Big Five personality traits and the ten
gamification factors. Marczewski [20] proposed the Hexad framework which has
six gamification user types that differ in their motivational factors. The
user types are personifications of people’s intrinsic (e.g. self-realization)
and extrinsic (e.g. rewards) motivations, as defined by the self-determination
theory [27]. Table 1 shows the gamification user types defined by the Hexad
framework as well as the motivations and characteristics of each user type
[20, 31]. Tondello et al. [32] proposed the 24-items survey response scale to
score the user’s preferences towards the six different motivations in the
Hexad framework. This measure has the potential to accurately measure user
preferences in gamification. There are four survey items related to each user
type, and all answers are rated on a 7-point Likert scale. The score of each
user type is obtained by adding the answers of each of the four questions, and
the highest score is the user type. Note that the Hexad user type is an
archetypical categorization where the types represent users for whom certain
motivations are stronger than other motivations.

Table 1: Gamification user types defined in the Hexad framework User types | Motivation | Characteristics
---|---|---
Philanthropist |  | Purpose
---
| They are altruistic and willing to give without expecting a reward.
---
Socialiser |  | Relatedness
---
| They want to interact with others and create social connections.
---
Free Spirit |  | Autonomy
---
| They like to create and explore within a system.
---
Freedom to express themselves and act without external control.
Achiever |  | Competence
---
| They seek to progress with a system by completing tasks,
---
or prove themselves by tackling different challenges.
Player |  | Extrinsic
---
rewards
| They will do whatever to earn a reward
---
within a system independently of the type of the activity.
Disruptor |  | Triggering
---
of change
| They tend to disrupt the system either
---
directly or through others to force negative
or positive changes.

##  3 Study Design

In this study, we investigate the impacts of different task allocation
interfaces on dynamic tourism information collection efficiency and tourism
satisfaction in gamified participatory sensing. In addition, we investigate
whether the degree of the contribution to sensing and the interface design
preferences are influenced by the individual personality. We first describe
the basic design, including the data to be collected and the assumed
environment, in the next section. After that, we describe the details of each
interface and its implementation in the application.

###  3.1 Basic design

The data to be collected by participatory sensing for tourist and the assumed
environment in this study are as follows. The data is dynamic tourism
information, specifically photos, comments and inertial sensor data built into
smartphones at the sightseeing attractions. With the development of human
activity recognition research, it is possible to collect information such as
tourist behaviors [25] and congestion degree in the surrounding area [7] from
sensor data collected from smartphones. Also, photos and comments are very
useful information for the next tourist to understand the current situation of
the sightseeing attraction. We use simple gamification mechanics, namely
missions, point-based rewards and ranking. Participants have our app installed
on their own smartphones and posting photos and comments at a specific tourist
attraction will appear on the app as a mission. Each time they perform the
mission while their sightseeing, the users will receive points as a reward
within the app. Ranking is determined among the app users and displayed on the
app, depending on the total amount of points. Based on prior work by Kawanaka
et al. [16], we use dynamic rewards that change according to the demand for
information at each spot. This is designed under the assumption that campaign
organizers (e.g. municipalities and tourism associations) can efficiently
collect tourist information on the sightseeing spots they need. In this study,
we designed two types of task (=mission) allocation interfaces based on these
environments. One is a map-based interface in which the task is selected
actively by the participant, and the other one is a chat-based interface in
which the task is selected semi-passively based on the suggestion of the chat
with agent character.

###  3.2 Task Allocation Interfaces

Map-based
In this interface, all the spots to be sensed are displayed on the map and the
user can accomplish the mission when actively checking the information of each
spot one by one. A screenshot of map-based interface is shown in Figure 1. The
pins displayed on the map are colored gold (high demand), silver (medium
demand), and copper (low demand) according to the information demand level.
The detailed information of each spot and the points are displayed by tapping
on the pins. The users can check-in by tapping the pin when they are a certain
distance away from the target spot. After that, the users can take a photo and
post it with comment to complete the check-in process and receive a point.

Chat-based
In this interface, the main screen is a chat-based dialogue with the agent
character and the user selects the mission during the interaction. A
screenshot of the chat-based interface is shown in 2. The agent asks the user
to do a mission and the user accepts the specific mission in the dialogue and
goes to the target spot to execute the mission. The algorithm for determining
the requested mission is as follows. The user’s current location is obtained
and the linear distance between all the spots and the user is calculated. The
ten closest spots are selected and sorted by points (the spot with the most
points gets the highest priority). At the beginning of the interaction, the
agent selects the sightseeing spot with the highest priority (according to the
algorithm) and asks the user to do this mission. Then, the user has three
choices (blue buttons at the bottom of the screen):

1

Okay, I will do this mission.

2

Do you have any alternatives?

3

Do you have any details of this spot?

In addition, by tapping the “Check Map” button on the chat screen, the
specific locations can be seen on the map. Through repeated dialogue, the
users receives a mission that they want to do, go to the target spot and
execute the mission. The process of executing the mission is the same as for
the map-based.

Additionally, we implemented Free posting as a common function to both
interfaces. This allows participants to freely post any information they find
of interest or want to share with other tourists while their sightseeing. Free
posting can be done by tapping the camera button at the bottom of the screen.

Figure 1: Map-based interface Figure 2: Chat-based interface

###  3.3 Communication Style Design in Chat-based Interface

As we mentioned in related research, when employing an interactive interface,
the conventional style may affect the data quality and user’s satisfaction. In
order to investigate the appropriate dialogue sentences and the effect on
mission selection by the sentences, we formulated four different types of
dialogue templates considering the communication styles elaborateness and
indirectness in the chat-based interface. The following templates were created
(The Japanese notation is added, since the experiment was conducted with only
Japanese participants):

Figure 3: Correspondence of each communication style and agent character

Elaborate & Direct(ED)

:
English : Go for mission ¡spot name¿. You can get ¡100¿ points and it is just
about ¡5¿ minutes from here. It is the ¡closest¿ spot from your current
location and the one where you can get the ¡most¿ points.
Japanese : ¡スポット名¿ へ行ってください！ここから約 ¡5¿で到着し、100 ポイントを獲得できます。現在地から
¡1¿番目に近いスポットで、¡1¿ 番目に多くポイントを獲得できるスポットです。

Elaborate & Indirect(EI)

:
English : You can get ¡100¿ points for mission ¡spot name¿ which is just about
¡5¿ minutes from here. It is the ¡closest¿ spot from your current location and
the one where you can get the ¡most¿ points.
Japanese : ここから約 ¡5¿分で到着する ¡スポット名¿ では ¡100¿ ポイントを獲得できます！ 現在地から ¡1¿
番目に近いスポットで、¡1¿ 番目に多くポイントを獲得できるスポットです。

Concise & Direct(CD)

:
English : Go for mission ¡spot name¿. You can get ¡100¿ points and it is just
about ¡5¿ minutes from here.
Japanese : ¡スポット名¿へ行ってください！ ここから約 ¡5¿ 分で到着し、¡100¿ ポイントを獲得できます。

Concise & Indirect(CI)

:
English : You can get ¡100¿ points for mission ¡spot name¿ which is just about
¡5¿ minutes from here.
Japanese : ここから約 ¡5¿ 分で到着する¡スポット名¿ では、¡100¿ ポイントを獲得できます！

To make each interaction style more distinguishable, the colour of the agent’s
clothing changes with the communication style as can be seen in Figure 3.

###  3.4 Application Implementation

We implemented these task allocation interfaces into the participatory sensing
platform application called Parmosense [21]. The timestamp, GPS, acceleration,
gyroscopic, geomagnetism, and illuminance values of the smartphone are
collected at a sampling rate of 10 Hz while this application is running (even
in the background). The data is sent to the server every 5 seconds. Sensor
data is also collected at the moment when the user takes a photo and is sent
to the server along with the captured photograph, independently of the
periodic sensor data.

##  4 Experiment

We conducted a tourism experiment to elucidate how the different interfaces
and user types affect the efficiency of data collection, tourism satisfaction,
and tourism behavior. In this chapter, we first describe the recruitment
procedure and the participants’ demographic information. After that, we
explain the experimental procedure and the contents of post-survey.

###  4.1 Participants

We recruited participants through research participant recruitment company.
Participants were limited to those who were Japanese, over 18 and under 80
years old, and living outside Nara Prefecture where the tourism experiment is
conducted. We asked to complete a questionnaire about the age, gender,
previous tourism experience in the experimental area, and user types using the
Hexad Gamification User Types Scale [31] during the application process.
Finally, there were 157 applicants, and 110 participants were selected based
on the results of the questionnaire on user types and tourism experience.
However, we describe the data and results from 108 participants because two of
them could not collect the data normally.

There were 50 male and 58 female and aged between 19 and 71 years
($M=41.0,SD=13.9$). With regard to the tourism experience, six people had
never visited the area before, and 28 people had visited it once. 26 people
had visited it twice and 49 people had visited it more than three times. In
terms of the Hexad gamification user types, 49 people as Free Spirit, 46
people were categorized as Philanthropist, 21 people as Player 17 people as
Socialiser and 14 people as Achiever (There were some participants with
multiple user types, the total number of user types exceeds 108.). Disrupter
were not included in this experiment. In this experiment, we divide the
experimental group into two: one group using the map-based interface and the
other group using the chat-based interface. The distribution of males and
females by age group and their tour experiences to Nara are shown in Figure 4.

(a) GroupA : Map-based interface

(b) Group B : Chat-based interface

Figure 4: User attributes for each experimental group Table 2: Number of participants by experimental group for each date Date |  Oct. 3rd |  26th |  28th |  31st |  Nov. 1st |  4th.
---|---|---|---|---|---|---
Group A |  4 |  10 |  11 |  11 |  9 |  8
Group B |  4 |  10 |  9 |  10 |  14 |  8
Total |  8 |  20 |  20 |  21 |  23 |  16

###  4.2 Experimental Procedure

The experiment was conducted in Nara, Japan in October 3rd, 26th, 28th, 31st,
November 1st, and 4th, 2020222This experiment is carried out with the approval
of ethics review committee of Nara Institute Science and Technology. In order
to prevent the spread of COVID-19, participants were required to 1. wear a
mask, 2. avoid long-term stays in crowded places, and 3. stop the experiment
immediately if they were not feeling well.. About 10 to 20 people were
assigned to each of the above dates, taking into account the available dates
of the participants. The number of participants for each dates were shown in
Table 2.

Detailed explanation of the experiment was given to the participants through
documents and any questions about experiment were accepted at any time. The
experimental application was installed on a participants’ own smartphone in
advance using TestFlight, a beta app delivery platform provided by Apple. The
use of the application was explained through documents and YouTube videos. On
the day of the experiment, the participants were gathered at the Kintestu-Nara
station as start point of the experiment, and we explained the overview of the
experiment, cautions on the experiment, and how to use the application one by
one. In addition, we answered individually to participants who had questions
on the experiment and how to use the application. The duration of the
experiment was four hours, and the participants used the assigned interface at
all times during the experiment. In the main session of the experiment, we
asked participants to do sightseeing alone and only on foot in the designated
areas, while accomplishing missions and earning points. After the sightseeing
experiment, participants answered to a post-survey about their tourism
behavior and satisfaction, the usability of the application, and impressions
throughout the experiment. The details of the post survey will be described in
Section 4.3. We paid each participant 8,000 yen ($\fallingdotseq$ 80 USD) as a
basic participation fee including transportation fee to the venue. This is
determined based on an hourly wage of 1,000 yen ($\fallingdotseq$ 10 USD),
taking into account the 4 hours of experimental time, time for questionnaire
response. In addition, since only people living outside Nara Prefecture were
targeted in this experiment, an additional 3,000 ($\fallingdotseq$ 30 USD) yen
was paid for round-trip transportation fee.

###  4.3 Post-survey

We conducted a post-survey to subjectively evaluate tourism behavior and
satisfaction and the usability of the application through the experiment. The
survey was divided into four categories: tourism satisfaction, interface
preference and communication styles, application usability, and impressions
throughout the experiment.

Tourism satisfaction: The tourism satisfaction was assessed by the following
questions on priorities between tourism and mission and the enjoyment of
tourism.

Q1

Which did you prioritize sightseeing or the mission?

Q2

Did the application make tourism more enjoyable for you?

For Q1, participants answered this question with a five-point Likert scale in
which 1 $=$ prioritized sightseeing and 5 $=$ prioritized the mission, and and
we asked the reason of their answers using an open question. In Q2, they also
answered this question with a five-point Likert scale in which 1 $=$ Not at
all fun and 5 $=$ Very fun, and we asked the reason of their answers using an
open question.

Interface preference and communication styles: In this experiment, each
participant used only one interface, so we asked them about their preference
for the interface app. For the communication style, we asked the participants
who used chat-based interface application if they noticed any differences in
sentences and which communication style they preferred, as follows.

Q3

Do you like the map-based/chat-based style user interface?

Q4

Did you notice any changes to the sentence or appearance in your interactions
with agents?

Q5

Which agent did you think was the best? Please pay attention to the sentence
and answer it.

For Q3, participants answered this question with a five-point Likert scale in
which 1 $=$Don’t like it at all and 5 $=$Like it very much, and and we asked
the reason of their answers using an open question. Q4 was answered with
binary option, yes or no, and Q5 was answered 1-4 options with sample
screenings shots pasted for each communication style; 1: Elaborate & Direct,
2: Elaborate & Indirect, 3: Concise & Direct, 4: Concise & Indirect.

Application usability: The application usability of each interface was
evaluated with System Usability Scale [2], which allows us to easily get the
usability score (min:0, max:100) of a system with ten questionnaire items.

Impressions throughout the experiment: Finally, we asked them for their
impressions throughout the tourism experiment with open questions.

##  5 Results

Through the whole experiment, approximately 1.53 GB of sensor data, 3148
photos and comments, and 108 post-survey answers were collected. In order to
investigate the impact of different task allocation interfaces on tourism
information collection efficiency, tourism behavior and tourism satisfaction
in participatory sensing for tourists, a quantitative evaluation using the
collected log data and a qualitative evaluation using the questionnaire
results were conducted.

###  5.1 Quantitative Evaluation using Collected Data

| Demand Level |  Free |
---|---|---|---
|  Low |  Middle |  High |  Posting |  Total
Total Posts |  562 |  470 |  480 |  290 |  1802
Average |  10.60 |  8.87 |  9.06 |  5.47 |  34.00
Median |  10 |  8 |  8 |  2 |  32
SD |  4.21 |  5.03 |  5.60 |  7.51 |  15.37
Table 3: Summary of the collected posts in map-based interface | Demand Level |  Free |
---|---|---|---
|  Low |  Middle |  High |  Posting |  Total
Total Posts |  166 |  258 |  532 |  390 |  1346
Average |  3.02 |  4.69 |  9.67 |  7.09 |  24.47
Median |  2 |  4 |  9 |  2 |  22
SD |  3.00 |  3.24 |  5.52 |  10.91 |  14.77
Table 4: Summary of the collected posts in chat-based interface Figure 5:
Check-in ratio according to the information demand level in large scale
experiment

The summary of the collected posts in the map-based interface and chat-based
interface are shown in Table 3 and Table 4, respectively. The 1512 posts
(average 28.5 posts per person) are submitted as check-in missions, the 290
posts (average 5.5 posts per person) are submitted as free posting and 1802
posts are obtained in total from map-based interface. On the other hand, the
956 posts (average 17.4 posts per person) are submitted as check-in missions,
the 390 posts (average 7.1 posts per person) are submitted as free posting and
1346 posts are obtained in total from chat-based interface. The absolute
number of posts obtained by the check-in mission was about 1.55 times greater
on average for the map-based interface. However, the absolute number of
submissions obtained by free posting was about 1.42 times greater on average
for the chat-based interface. When both were combined, the posts was about
1.39 times greater on average for the map-based interface.

A statistical significance test was performed to determine if there is a
significant difference for differences in the number of posts obtained for
each interface. First, we performed a Shapiro-Wilk test to check the normality
of the number of posts obtained in the check-in mission and free posting at
each interface. The results show that the total number of accomplished
missions for the chat-based interface follows normality ($p=0.22$), but the
rest does not follow. We therefore ran a Mann-Whitney U Test to compare the
number of missions completed by each participant and the number of free
postings by each participant. As a result, we found significant differences
only between the posts obtained for the check-in missions in each interface.
We found that the number of posts from the check-in missions was significantly
greater in the map-based interface. On the other hand, the average number of
posts obtained from free posting was grater for the chat-based interface, but
the significant difference was not found.

(a) Four communication styles (b) Elaborateness and Indirectness
---
Figure 6: Check-in rate by communication style in chat-based interface

Next, the quality of the data was evaluated by the check-in ratio according to
the information demand of each sightseeing attraction. The check-in ratio
according to information demand level in each interface is shown in Figure 5.
In the map-based interface, the rate was the highest for the low-demand spots,
which are colored with bronze and assigned to more famous spots. On the other
hand, the participants were more likely to complete in the high-demand spots
colored with gold.

Finally, we will elucidate whether the efficiency of data collection differs
depending on the communication style in the chat-based interface. Figure 6
shows the check-in ratio for each communication style; the results are shown
for each of the four communication styles in (a), and the results are
tabulated for each dimension of Elaborateness and Indirectness in (b). In
Figure 6 (a), the ratio of high demand missions in Elaborate & Indirect and
Direct & Concise is slightly higher, but similar results are obtained in
almost all styles. In addition, similar results were also obtained for all
items when we see the results from the two dimensions in (b).

(a) The distribution of answers (b) Average score
---
Figure 7: Summary of the answers to Q1 on the priority of mission and
sightseeing (a) The distribution of answers (b) Average score
---
Figure 8: Summary of the answers to Q2 on the sightseeing enjoyment

###  5.2 Quantitative Evaluation using Post-survey

Tourism satisfaction: The summary of the answers to Q1 on priorities between
tourism and mission is shown in Figure 7; (a) shows the distributions of
answers for each interface and (b) shows the average score of the answers. The
average and median scores for the map-based interface were 3.44 and 4.00
($S.D.=1.37$), and for the chat-based interface were 4.04 and 4.00
($S.D.=1.05$). This result shows that missions are prioritized over tourism in
both interfaces. It was also found that there is a tendency to prioritize
missions over map-based interface in the chat-based interface. To determine if
this difference is statistically significant, we performed a significance
test. The normality of the answers to Q1 for each interface was confirmed by
the Shapiro-Wilk test, and the results both did not follow a normal
distribution. Therefore, we used the Mann–Whitney U test, and we found a
significant difference between them ($p<0.05$). We found that tourists are
significantly more likely to prioritize missions with the chat-based interface
than with the map-based interface.

Next, we summarize the results obtained by free description of the reasons for
the responses. In the map-based interface, the most common reason given by the
participants who answered 5 or 4, i.e., who more prioritized the mission, was
the “Gameplay”, with 17 participants answering. For example, the participant
P71 (Female, 46) responded, “I wanted to go to the place with the highest
points as much as possible because it became fun like a game.” and the
participant P66 (Male, 48) answered, “I was focusing on sightseeing until the
middle of the tour, but since I’m the type of person who wants to compete when
I’m given a ranking, so I became mission-oriented from the middle.” The second
most common answer was “For sightseeing reference”, with 6 respondents. On the
other hand, 15 participants answered, “For sightseeing reference”, which was
the most common reason for prioritizing missions in the chat-based interface.
For instance, the participant P29 (Female, 22) responded, “I thought there
would be many places that I could only learn about through the app,” and
Participant P49 (female, 21) responded, “I didn’t know this area well, so I
followed the mission to go sightseeing.”. The second most common answer was
“Gameplay”, with 10 respondents. In addition, as a characteristic answer of
the chat-based, 8 people answered “Sense of duty”, and as an example, the
participant P47 (Female, 45) answered “Because the agent character asked me
the mission.”.

These responses indicate that in the map-based interface, gamification
elements such as points and ranking were the factors that made people
prioritize the mission more. In the chat-based interface, the passivity of
asking a spot and the algorithm of prioritizing minor spots with high
information demand were found to be factors.

The answers to Q2 on sightseeing enjoyment are summarised in Figure 8; (a)
shows the distribution of answers for each interface and (b) shows the average
score of the answers. The average and median scores for the map-based
interface were 3.87 and 4.00 ($S.D.=0.99$), and for the chat-based interface
were 3.58 and 4.00 ($S.D.=1.03$). This result shows that both interfaces make
tourism more enjoyable. It was also found that the map-based interface tend to
make tourism more fun than the chat-based interface. Similarly, we conducted a
significance test to determine if there is a significant difference. We used
the the Mann–Whitney U test, since the results of the Shapiro-Wilk test did
not follow a normal distribution. The results of test showed that there is no
significant difference between the enjoyment of sightseeing with the chat-
based interface and with the map-based interface ($p=0.10$). That is, the
enjoyment of tourism does not differ significantly between the different
interfaces.

Next, we summarize the reasons for the answers regrading enjoyment. The most
common answer for the participants who answered 5 or 4, i.e., who responded
that they enjoyed sightseeing more than usual, was “Chance encounter”, with 17
and 22 participants in the map-based and chat-based, respectively. For
example, Group A participant P70 (Male, 69) responded, “I went to places I
would not have normally gone to, but there were spots nearby. This leads to
awareness.” and Group B participant P58 (Male, 22) answered “I was able to
visit minor places that I would not have chosen on my own.”. The reason for
the larger number of respondents in the chat-based interface, it is assumed
that lesser-known spots are preferentially requested by agent characters. The
second most mentioned factor was “Gameplay”, with 9 and 6 respondents,
respectively. The examples are follows, Group A participant P76 (Male, 24)
mentioned, “I thought I would sightseeing would be neglected, but I felt a
sense of accomplishment by visualizing the trip with points and recorded the
places I visited.” and Group B participant P102 (Male, 39) answered,
“Normally, it takes time to decide a tourist spot, but I felt that I was able
to go around a lot by making it a mission by this application. ”.

(a) The distribution of answers (b) Average score
---
Figure 9: Summary of the answers to Q3 on the interface preference Figure 10:
The answers to Q4 on whether the participants noticed the differences of
sentence and appearance of agent characters

Interface and communication style preferences: The summary of the answers to
Q3 on interface preference is shown in Figure 9. The mean $M$ and the median
$Md$ for the map-based interface are $M(m)=3.69$ and $Md(m)=4.00$, the results
for the chat-based interface are $M(c)=3.29$ and $Md(c)=3.00$. There is a
statistically significant difference between $M(m)$ and $M(c)$ ($p=0.03$ using
the Mann-Whitney-U-Test), showing that the participants prefer the map-based
interface over the chat-based interface.

26 participants (47 %) noticed a difference in the agent’s interaction, while
29 participants (53 %) did not notice any difference. The gender distribution
is shown in Figure 10. This result indicates that the female participants were
more sensitive to the changes in the agent’s communication style. However,
there is no significant difference (using a Chi-Squared Test).

---
Figure 11: The result of Q5, showing the communication style preferences of
all participants ($N=55$).
---
Figure 12: The result of Q5, showing the communication style preferences of
all participants who noticed a difference in the agent’s interaction ($N=26$).

Figure 11 shows the communication style preferences of all participants
($N=55$) and Figure 12 shows the communication style preferences of all
participants who noticed a difference in the agent’s interaction ($N=26$). It
can be seen that there is a clear preference in the elaborateness dimension,
both when looking at all participants and when looking at only those
participants who noticed a difference in the agent’s interaction. A Chi-
Squared Test shows that the difference between elaborate and concise is
statistically significant for both groups ($p<0,05$). Hence, the participants
significantly preferred the elaborate communication style over the concise
one. This shows that, in general, more detailed information is preferred for
the task at hand. However, it has to be noted that this does not apply to all
participants. Some of them clearly stated that they find a short and simple
text easier to read on the smartphone while walking. Moreover, there is no
preference for the indirectness dimension. This is in line with the results
presented in [23], that there is no general preference in the system’s
communication style and therefore the preference appears to be individual for
every person.

Application usability: The summary of the applixation usability evaluation
using SUS score is shown in Figure 13; (a) shows the average SUS score by age
group and (b) shows the overall average score of the answers. The average and
median SUS scores for the map-based interface were 75.6 and 75.0
($S.D.=12.7$), and for the chat-based interface were 64.3 and 67.5
($S.D.=17.6$). In order to clarify whether there is a significant difference
between them, the Mann-Whitney U test was performed since each SUS score did
not follow normality in each interface and a significant difference was found
between them ($p<0.01$). That is, the map-based interface was found to be a
significantly more usable interface than the chat-based interface. Next, in
order to clarify the items that affected the difference in usability, the Man-
Wittny U test was conducted to the responses for each of ten items. Figure 14
shows the average score for each of the ten items in each interfaces, and
items for which significant differences were found are indicated by asterisks
on the bars. As a result, significant differences were found for questionnaire
items Q1 ($p<0.05$), Q2 ($p<0.01$), Q3 ($p<0.001$), Q6 ($p<0.05$), Q7
($p<0.01$), and Q8 ($p<0.05$). Items Q2, Q3, and Q8 are related to complexity
of application, and the scores for all items were more positive for the map-
based interface. Item Q6 is related to consistency of the application and the
Q7 is related the need for training until they can use the app, and the all
scores were more positive for the map-based interface as well. Due to these
results, the map-based interface scored higher in Q1 about if they want to use
this app frequently. On the other hand, the items that did not find
significant differences were Q4 and Q10 regarding the needs for support, Q5
regarding the consistency of the app, and Q9 regarding the confidence for
using the app. That is, there was no difference in the degree to which the
users could use the application confidently without support once they start
using the application, regardless of the interface.

(a) Average SUS score by age group (b) Total average score
---
Figure 13: Summary of the application usability evaluation using SUS score
Figure 14: The average score for each of the ten items in each interface

Impressions through the experiment The following is examples of the free
description impressions through the experiment. First we sum up the coments
given from the participants who used map-based interface. Participant
P23(Female, 46) answered, “Thanks to the app, I was able to visit places for
the first time and know the places where I want to go in the next time, and I
enjoyed sightseeing.”. P32(Female, 32) responded, “I could know there are
various tourist spots, but I sometimes could not concentrate on one tourist
spot because I thought like “I want to go here! and there too!”. However, I
was able to continue to enjoy sightseeing in Nara without getting bored.” P70
(Male, 69) mentioned, “I’ve been to Nara before, but I was able to find out
places I didn’t know through this experiment. I felt that if I could enjoy
sightseeing with this app in the future, I would want to go to more places.”.
Some of participants gave us the another aspect of views, like “Group travel
is often avoided with this Corona situation, but I think this app can be a new
way to share the joy of sightseeing.” from participant P69 (Female, 42).

The following is the feedback that we got from the chat-based interface. P38
(Female, 22) responded, “I became attached to Nara, through this experiment.
Additionally, I’ve been Nara several times before, but I became more familiar
in this time. I felt a little lonely because I was sightseeing alone, but it
was good to be able to go around at my own pace. In addition to famous
sightseeing spots, I was able to visit tourist spots that I didn’t know or
passed by if they weren’t displayed in the app, and it was good to study
history.” P50 (Male, 57) answered, “I had a meaningful experience in a place I
didn’t know well.” P77 (Female, 46) mentioned, “I was able to meet new places
and beautiful scenery, and after reading the explanation of the points, I
became more and more interested in Nara, thanks to this experiment. I arrived
at my destination with peace of mind even on narrow roads, thanks to this app.
I would like you to make it at other tourist spots. I think it would be great
if a multilingual version was made and could be used by foreign tourists.” In
addition, as a characteristic opinion in the chat-based interface, the
following answer is obtained from Participant P49 (Female, 22) ; “Even though
I was sightseeing alone, it was fun to feel like I wasn’t alone while using
the application.”.

As mentioned above, most of the impressions obtained through the experiment
were positive, but some participants gave us the following opinions.
Participant P95 (Male, 34, Map-based) mentioned, “With the points and rankings
displayed on the app, I tried my best and walked too much.”. Participant P61
(Female, 20, Chat-based) described, “It was better for me to have no guidance.
However, I think it was good that game elements such as ranking format were
incorporated.”

###  5.3 Correlation between Behaviours and User Types

Here, we clarify whether there are differences in data collection
characteristics, tourism satisfaction, and interface preferences depending on
the personality and user type of the participants. The responses obtained by
the 5-likert scale in the post-survey is used as an interval scale, and
Pearson’s product-moment correlation and test of Non-correlations will be
used. The significance level is set at $p<0.05$, and $0.1>p>0.05$ is
considered as marginally significant. First, we discuss the correlation with
the data collection tendency. We found a weak negative correlation and a
marginally significant with Free Spirit in the map-based interface
($r=-0.26,p=0.06$). In the total number of postings including free postings,
there was also a weak negative correlation and significant difference with
Free Spirit ($r=-0.38,p<0.01$). When calculated the correlation with all free
postings, no correlation or significant difference was found. However, a weak
positive correlation and significant difference between the number of free
postings and Philanthropist was found when the test was performed on the
number of free postings of participants who had posted at least once
($r=0.34,p<0.01$). This tendency was similar when tested with the map-based
($r=0.40,p<0.01$) and chat-based ($r=0.32,p=0.05$) interfaces respectively.

Next, we describe the correlation with tourism satisfaction. In the chat-based
interface, a weak negative correlation and a marginally significant were found
between tourism priority and Free Spirit ($r=-0.24,p=0.08$). In terms of
tourism enjoyment, there was a weak positive correlation and a significant
difference in the attribute value of Player in the Map-based interface
($r=0.37,p<0.01$).

Finally, we discuss the correlation with interface preference. Weak positive
correlation and marginally significant between interface preferences and
Player were found for the map-based interface ($r=0.25,p=0.07$). In the chat-
based interface, a weak positive correlation and a marginally significant were
found with Achiever ($r=0.26,p=0.05$).

##  6 Discussion

In this section, we discuss the answers to our research questions based on the
results obtained through the large scale experiment.

RQ1: How does the different task allocation interfaces affect the quantity and
quality of dynamic tourism information collection?

Regarding the quantity of the collected data, the map-based interface could
collect about 1.4 times, and we found a significant difference between the
interfaces. In the map-based interface, all the spots are visible at the same
time, so it is possible to make a detour to other mission on the way to a
certain destination. On the other hand, only the spots that have been decided
in the chat dialogue are shown on the map in the chat-based interface. The
difference in the amount of data is attributed to the difference in the
characteristics of the interface. Another possible reason is that the chat-
based interface requires more procedures than the map-based interface, as
shown by the significant difference in the complexity of application in the
SUS evaluation. On the other hand, the chat-based interface could collect the
high-demand data preferentially and efficiently. This result is caused by the
fact that the chat-based interface uses an algorithm that prioritizes requests
for spots with high points (high information demand) based on location
information.

(a) Map-based (b) Chat-based
---
Figure 15: The correspondence table between Q1:priority and Q2:enjoyment

RQ2: Do the different task allocation interfaces have an impact on tourism
satisfaction of the tourists?

From questionnaire Q1 and Q2, it was found that the mission was significantly
more prioritized in the chat-based interface, but the interface difference did
not affect the impact on the enjoyment of sightseeing. The correspondence
table between Q1: priority and Q2: enjoyment is shown in Figure 15. This
result shows that the map-based interface has become a factor that makes
sightseeing more enjoyable while balancing sightseeing and missions. The same
tendency can be seen in the chat-based interface, but the participants more
prioritized to the mission. This result suggests that a certain sense of
responsibility might be generated through agent interaction in chat.

RQ3: Is there a relationship between tourism information collection efficiency
and interface preference, and gamification user type?

First, we describe the difference in data collection efficiency by user type.
A negative correlation was found between the number of mission posts and the
Free Spirit attribute value in the map-based interface. Free Spirit is a user
type that is motivated by autonomy and is not constrained by external control.
It is assumed that participants with high autonomy might grasp missions as
external controls and tend to perform them less frequently, while participants
with relatively low autonomy tend to follow the missions and perform them more
frequently. Additionally, there was a negative correlation between Free Spirit
and priority of sightseeing although in chat-based interface. From these
results, it is considered that the tendency to prioritize tourism and missions
differs depending on the degree of autonomy, and participants with higher
autonomy are more likely to prioritize their own tourism, resulting in a
decrease in the number of posts. On the other hand, there was a positive
correlation between Philanthropist attribute value and the number of free
posting, which allows participants to actively post at their own timing during
sightseeing and obtains fewer points. Philanthropists focus on purpose as
their motivation and tend to act altruistically without the extrinsic rewards.
The number of free postings for the purpose of sharing the situation in the
tourist attractions with the other participants is quite large, as shown in
the open-ended responses for the purpose of free posting, such as “when I find
a place that is dangerous for people using the app or something I have never
seen before” (P2, Female, 38, Map-based), “when I find a place that I want
everyone to visit. (P25, Male, 28, Chat-based). These factors suggest that
users with high Philanthropists’ attribute values tend to post more in order
to share their situations at sightseeing spots with other participants by free
posting and solving the timeline. As examples of the reason for free posting,
we obtained such comments, “To tell people about dangerous places. Or when I
find something I have never seen before.” (P2, Female, 38, Map-based), “ When
I found a place that I wanted everyone to visit. ” (P25, Male, 28, Chat-
based). These results suggest that participants with high Philanthropist
attribute value tend to post more in order to share their situations at
tourist attractions to other participants through free posts and timelines.

Next, we discuss the relationship between interface preference and user type.
There was a positive correlation with the Player attribute value in the map-
based interface. Players are mainly motivated by extrinsic rewards and will
try to earn rewards from the system regardless of the type of activity. In the
map-based interface, all missions can be seen on a map, and they can see at a
glance that the points to be obtained differ depending on the spot. Therefore,
it is expected to stimulate the motivation of Player users who try to obtain
higher points. We found also a positive correlation between the enjoyment of
sightseeing and the Player attribute value in map-based interface. That is,
participants with a high Player value visit spots where they can get higher
points, and enjoy sightseeing more while getting points, which may have
increased their preference for the map-based interface. On the other hand,
there was a positive correlation with Achiever attribute value in the chat-
based interface. Achiever is mainly motivated by competence and seeks to
perform the task given by the system. In the chat-based interface, the agent
character asks the participant to go to the spot where the system needs
information as needed. Therefore, it is considered that participants with high
Achiever attribute value are more motivated to complete the given missions one
after another, which in turn increases their preference for the chat-based
interface.

RQ4: What is the impact of different communication style sentences in a chat-
based interface?

47 % of the participants noticed a difference in the agent’s communication
style, showing that a large number of participants were aware of these subtle
changes. Moreover, the results show that there is a clear preference in the
elaborateness dimension, both when looking at all participants and when
looking at only those participants who noticed a difference in the agent’s
interaction. The participants significantly preferred the elaborate
communication style over the concise one. This shows that, in general, more
detailed information is preferred for the task at hand. However, this does not
apply to all participants. Some of them clearly stated that they find a short
and simple text easier to read on the smartphone while walking. Moreover,
there is no preference for the indirectness dimension. This is in line with
the results presented in [23], that there is no general preference in the
system’s communication style and therefore the preference appears to be
individual for every person.

##  7 Conclusion

The purpose of this paper was to investigate the effects of task allocation
interfaces and user types on tourist information collection efficiency,
tourist behavior, and tourist satisfaction in a gamified participatory sensing
for tourists. We designed and implemented two types of task allocation
interfaces (map-based and chat-based), and we used four different
communication styles based on two dimensions, elaborateness and indirectness,
to elucidate the appropriate dialogue requests in the chat-based interface.
For gamification user modeling, we introduced the Hexad gamification user type
which defined by Tondello et al. [32]. Then, we set four research questions
and these were clarified through a large-scale sightseeing experiments with
108 ordinary people aged between 19 and 71 in Nara. We found the following
through from the experiment. The absolute number of contributions was about
1.4 times greater for the map-based interface than the chat-based interface,
but it was more efficient in obtaining the data required by the system. In
addition, there was no significant difference in the tourism satisfaction
between the two interfaces. However, we found different trends for the
contribution to sensing and the interface preference by user type. As for the
free posting, there was a positive and weak correlation between the number of
contributions and the Philanthropist attribute value for the participants who
posted more than one contribution. That is, the higher the value of
Philanthropy, the higher the number of free contributions. There was no
significant difference in the impact of the different interfaces on the
enjoyment of tourism. On the other hand, the usability of the application was
higher for the map-based interface in terms of SUS score. When evaluating the
different communication styles of the chat-based interface, we could show that
47 % of the participants noticed a difference in the agent’s communication
style. Hence, a large number of participants were aware of these subtle
changes. Furthermore, the participants significantly preferred the elaborate
communication style over the concise one. However, there is no preference for
the indirectness dimension. This shows that there is no general preference in
the system’s communication style and therefore the preference appears to be
individual for every person. The overall impression of the experiment was
generally positive, for example, that using minor tourist attractions as
checkpoints would give a sense of serendipity to tourism.

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##  Appendix A Gamification User Types Hexad scale

Hexad is a gamification user type model consisting of six types to personalize
the gamification design according to the user’s personality [20, 32]. The
Gamification User Types Hexad scale is a 24-items survey response scale to
score users’ preferences towards the six different motivations in the Hexad
framework [31]. We asked the participants to rate how well each item describes
them in a 7-point Likert scale ; 1: Strongly disagree and 7: Strongly agree;
without identifying the corresponding type. The user type scores are
calculated that separately add the scores of the items corresponding to each
subscale. Basically, the one with the highest value in each subscale is used
as the representative user type, but it is an archetypical categorization in
Hexad framework.

Table 5: The Gamification User Types Hexad scale User Types | # |  English Items
---|---|---
Philanthropist | P1 |  It makes me happy if I am able to help others.
| P2 |  I like helping others to orient themselves in new situations.
| P3 |  I like sharing my knowledge.
| P4 |  The well being of others is important to me.
Socialiser | S1 |  Interacting with others is important to me.
| S2 |  I like being part of a team.
| S3 |  It is important to me to feel like I am part of a community.
| S4 |  I enjoy group activities.
Free Spirit | F1 |  It is important to me to follow my own path.
| F2 |  I often let my curiosity guide me.
| F3 |  I like to try new things.
| F4 |  Being independent is important to me.
Achiever | A1 |  I like defeating obstacles.
| A2 |  It is important to me to always carry out my tasks completely.
| A3 |  It is difficult for me to let go of a problem before I have found a solution.
| A4 |  I like mastering difficult tasks.
Player | R1 |  I like competitions where a prize can be won.
| R2 |  Rewards are a great way to motivate me.
| R3 |  Return of investment is important to me
| R4 |  If the reward is sufficient I will put in the effort.
Disruptor | D1 |  I like to provoke.
| D2 |  I like to question the status quo.
| D3 |  I see myself as a rebel.
| D4 |  I dislike following rules.

##  Appendix B System Usability Scale (SUS)

The SUS is a simple, ten-item scale giving a global view of subjective
assessments of usability [2]. It is calculated with following questionnaire
items. The questionnaire is answered with 5 point Likert scale; 1: Strongly
disagree and 5: Strongly agree.

  1. 1.

I think that I would like to use this system frequently.

  2. 2.

I found the system unnecessarily complex.

  3. 3.

I thought the system was easy to use.

  4. 4.

I think that I would need the support of a technical person to be able to use
this system.

  5. 5.

I found the various functions in this system were well integrated.

  6. 6.

I thought there was too much inconsistency in this system.

  7. 7.

I would imagine that most people would learn to use this system very quickly.

  8. 8.

I found the system very cumbersome to use.

  9. 9.

I felt very confident using the system.

  10. 10.

I needed to learn a lot of things before I could get going with this system.

To calculate the SUS score, first sum the score contributions from each item.
Each item’s score contribution will range from 0 to 4. For items 1,3,5,7,and 9
the score contribution is the scale position minus 1. For items 2,4,6,8 and
10, the contribution is 5 minus the scale position. Multiply the sum of the
scores by 2.5 to obtain the overall value of SUS.