Source author record

Kijung Kim

Explore this author’s publications, collaborators and research topics. This catalog record has not been claimed by its author.

ResearcherUnclaimed source record

math.CO Discrete Mathematics math.GR math.RA Computer Vision math.RT

Catalog footprint

Research overview

13works

6topics

4close collaborators

Actions

Is this your work?

Open graph Browse papers

preprint2026arXiv

Initiation of Interaction Detection Framework using a Nonverbal Cue for Human-Robot Interaction

This paper describes an initiation of interaction(IoI) detection framework without keywords for human-robot interaction(HRI) based on audio and vision sensor fusion in a domestic environment. In the proposed framework, the robot has its own audio and vision sensors, and can employ external vision sensor for stable human detection and tracking. When the user starts to speak while looking at the robot, the robot can localize his or her position by its sound source localization together with human tracking information. Then the robot can detect the IoI if it perceives the face of the speaker faces the robot. In case that the user does not speak directly, the robot can also detect the IoI if he or she looks at the robot for more than predefined periods of time. A state transition model for the proposed IoI detection framework is designed and verified by experiments with a mobile robot. In order to implement and associate our model in a robot architecture, all the components are implemented and integrated in the Robot Operating System(ROS) environment.

preprint2021arXiv

Restrained Italian domination in trees

Let $G=(V,E)$ be a graph. A subset $D$ of $V$ is a \textit{restrained dominating set} if every vertex in $V \setminus D$ is adjacent to a vertex in $D$ and to a vertex in $V \setminus D$ . The \textit{restrained domination number}, denoted by $γ_r(G)$ , is the smallest cardinality of a restrained dominating set of $G$ . A function $f : V \rightarrow \{0, 1, 2\}$ is a \textit{restrained Italian dominating function} on $G$ if (i) for each vertex $v \in V$ for which $f(v)=0$ , it holds that $\sum_{u \in N_G(v)} f(u) \geq 2$ , (ii) the subgraph induced by $\{v \in V \mid f(v)=0 \}$ has no isolated vertices. The \textit{restrained Italian domination number}, denoted by $γ_{rI}(G)$ , is the minimum weight taken over all restrained Italian dominating functions of $G$ . It is known that $γ_r(G) \leq γ_{rI}(G) \leq 2γ_r(G)$ for any graph $G$ . In this paper, we characterize the trees $T$ for which $γ_r(T) = γ_{rI}(T)$ , and we also characterize the trees $T$ for which $γ_{rI}(T) = 2γ_r(T)$ .

preprint2020arXiv

The Italian bondage and reinforcement numbers of digraphs

An \textit{Italian dominating function} on a digraph $D$ with vertex set $V(D)$ is defined as a function $f : V(D) \rightarrow \{0, 1, 2\}$ such that every vertex $v \in V(D)$ with $f(v) = 0$ has at least two in-neighbors assigned $1$ under $f$ or one in-neighbor $w$ with $f(w) = 2$ . The \textit{weight} of an Italian dominating function $f$ is the value $ω(f) = f(V(D)) = \sum_{u \in V(D)} f(u)$ . The \textit{Italian domination number} of a digraph $D$ , denoted by $γ_I(D)$ , is the minimum taken over the weights of all Italian dominating functions on $D$ . The \textit{Italian bondage number} of a digraph $D$ , denoted by $b_I(D)$ , is the minimum number of arcs of $A(D)$ whose removal in $D$ results in a digraph $D'$ with $γ_I(D') > γ_I(D)$ . The \textit{Italian reinforcement number} of a digraph $D$ , denoted by $r_I(D)$ , is the minimum number of extra arcs whose addition to $D$ results in a digraph $D'$ with $γ_I(D') < γ_I(D)$ . In this paper, we initiate the study of Italian bondage and reinforcement numbers in digraphs and present some bounds for $b_I(D)$ and $r_I(D)$ . We also determine the Italian bondage and reinforcement numbers of some classes of digraphs.

preprint2020arXiv

The Italian domination numbers of some products of directed cycles

An Italian dominating function on a digraph $D$ with vertex set $V(D)$ is defined as a function $f : V(D) \rightarrow \{0, 1, 2\}$ such that every vertex $v \in V(D)$ with $f(v) = 0$ has at least two in-neighbors assigned $1$ under $f$ or one in-neighbor $w$ with $f(w) = 2$ . In this paper, we determine the exact values of the Italian domination numbers of some products of directed cycles.

preprint2016arXiv

On commutative $p$ -schemes of order $p^4$

In this article, we consider the existence and schurity problem on commutative $p$ -schemes of order $p^4$ . Using the thin radical and thin residue, we give sufficient conditions for such $p$ -schemes to be schurian. We also give questions related to our results.

preprint2015arXiv

A family of non-Schurian $p$ -Schur rings over groups of order $p^3$

Recently, it was proved that every commutative $p$ -Schur ring over a group of order $p^3$ is Schurian. In this article, we consider the Schurity problem of non-commutative $p$ -Schur rings over groups of order $p^3$ . In particular, it is given a family of non-Schurian $p$ -Schur rings over groups of order $p^3$ .

preprint2015arXiv

Association schemes in which the thin residue is an elementary abelian $p$ -group of rank $2$

In this article, we investigate the existence and schurity problem of association schemes whose thin residues are isomorphic to an elementary abelian $p$ -group of rank $2$ .

preprint2015arXiv

Isomorphism classes of association schemes induced by Hadamard matrices

Every Hadamard matrix $H$ of order $n > 1$ induces a graph with $4n$ vertices, called the Hadamard graph $Γ(H)$ of $H$ . Since $Γ(H)$ is a distance-regular graph with diameter $4$ , it induces a $4$ -class association scheme $(Ω, S)$ of order $4n$ . In this article we deal with fission schemes of $(Ω, S)$ under certain conditions, and for such a fission scheme we estimate the number of isomorphism classes with the same intersection numbers as the fission scheme.

preprint2015arXiv

Terwilliger algebras of wreath products by 3-equivalent schemes

Recently G. Bhattacharyya, S.Y. Song and R. Tanaka began to study Terwilliger algebras of wreath products of one-class association schemes. K. Kim determined the structure of Terwilliger algebras of wreath products by one-class association schemes or quasi-thin schemes. In this paper, we study Terwilliger algebras of wreath products by $3$ -equivalenced schemes.

preprint2012arXiv

On $p$ -schemes of order $p^3$

Let $(X,S)$ be a $p$ -scheme of order $p^3$ and $T$ the thin residue of $S$ . Now we assume that $T$ has valency $p^2$ . It is easy to see that one of the following holds: (i) $|T|=p^2$ and $T\simeq C_{p^2}$ ; (ii) $|T|=p^2$ and $T\simeq C_p\times C_p$ ; (iii) $|T|<p^2$ . It is known that $(X,S)$ is Schurian if (i) holds. If (ii) holds, we will show that $(X,S)$ induces a partial linear space on $X/T$ . Moreover, the character degrees of $(X,S)$ coincide with the sizes of the lines of the partial linear space. Under the assumption (iii) we will show a construction of non-Schurian $p$ -schemes which are algebraically isomorphic to a Schurian $p$ -scheme of order $p^3$ .

preprint2012arXiv

On a conjecture of Brouwer involving the connectivity of strongly regular graphs

In this paper, we study a conjecture of Andries E. Brouwer from 1996 regarding the minimum number of vertices of a strongly regular graph whose removal disconnects the graph into non-singleton components. We show that strongly regular graphs constructed from copolar spaces and from the more general spaces called $Δ$ -spaces are counterexamples to Brouwer's Conjecture. Using J.I. Hall's characterization of finite reduced copolar spaces, we find that the triangular graphs $T(m)$ , the symplectic graphs $Sp(2r,q)$ over the field $\mathbb{F}_q$ (for any $q$ prime power), and the strongly regular graphs constructed from the hyperbolic quadrics $O^{+}(2r,2)$ and from the elliptic quadrics $O^{-}(2r,2)$ over the field $\mathbb{F}_2$ , respectively, are counterexamples to Brouwer's Conjecture. For each of these graphs, we determine precisely the minimum number of vertices whose removal disconnects the graph into non-singleton components. While we are not aware of an analogue of Hall's characterization theorem for $Δ$ -spaces, we show that complements of the point graphs of certain finite generalized quadrangles are point graphs of $Δ$ -spaces and thus, yield other counterexamples to Brouwer's Conjecture. We prove that Brouwer's Conjecture is true for many families of strongly regular graphs including the conference graphs, the generalized quadrangles $GQ(q,q)$ graphs, the lattice graphs, the Latin square graphs, the strongly regular graphs with smallest eigenvalue -2 (except the triangular graphs) and the primitive strongly regular graphs with at most 30 vertices except for few cases. We leave as an open problem determining the best general lower bound for the minimum size of a disconnecting set of vertices of a strongly regular graph, whose removal disconnects the graph into non-singleton components.

preprint2012arXiv

Terwilliger algebras of wreath products by quasi-thin schemes

The structure of Terwilliger algebras of wreath products by thin schemes or one-class schemes was studied in [A. Hanaki, K. Kim, Y. Maekawa, Terwilliger algebras of direct and wreath products of association schemes, J. Algebra 343 (2011) 195--200]. In this paper, we will consider the structure of Terwilliger algebras of wreath products by quasi-thin schemes. This gives a generalization of their result.

preprint2011arXiv

On wreath products of cyclic schemes

We describe explicitly the algebraic structure of the Terwilliger algebra of wreath products of cyclic schemes.

Inspect adjacent papers, topics, institutions and collaborators without losing the researcher page.

Building this map preview

BZPEER is loading the nearby papers, people, topics and institutions for this page.

Kijung Kim

Research overview

Is this your work?

13 publications

Initiation of Interaction Detection Framework using a Nonverbal Cue for Human-Robot Interaction

Restrained Italian domination in trees

The Italian bondage and reinforcement numbers of digraphs

The Italian domination numbers of some products of directed cycles

On commutative $p$ -schemes of order $p^4$

A family of non-Schurian $p$ -Schur rings over groups of order $p^3$

Association schemes in which the thin residue is an elementary abelian $p$ -group of rank $2$

Isomorphism classes of association schemes induced by Hadamard matrices

Terwilliger algebras of wreath products by 3-equivalent schemes

On $p$ -schemes of order $p^3$

On a conjecture of Brouwer involving the connectivity of strongly regular graphs

Terwilliger algebras of wreath products by quasi-thin schemes

On wreath products of cyclic schemes

See the researcher in context

Building this map preview

Kijung Kim

Research overview

Is this your work?

13 publications

Initiation of Interaction Detection Framework using a Nonverbal Cue for Human-Robot Interaction

Restrained Italian domination in trees

The Italian bondage and reinforcement numbers of digraphs

The Italian domination numbers of some products of directed cycles

On commutative ppp-schemes of order p4p^4p4

A family of non-Schurian ppp-Schur rings over groups of order p3p^3p3

Association schemes in which the thin residue is an elementary abelian ppp-group of rank 222

Isomorphism classes of association schemes induced by Hadamard matrices

Terwilliger algebras of wreath products by 3-equivalent schemes

On ppp-schemes of order p3p^3p3

On a conjecture of Brouwer involving the connectivity of strongly regular graphs

Terwilliger algebras of wreath products by quasi-thin schemes

On wreath products of cyclic schemes

See the researcher in context

Building this map preview

On commutative $p$ -schemes of order $p^4$

A family of non-Schurian $p$ -Schur rings over groups of order $p^3$

Association schemes in which the thin residue is an elementary abelian $p$ -group of rank $2$

On $p$ -schemes of order $p^3$