• 대한수학회지
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• 제49권3호
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• pp.475-491
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• 2012

In 1950 a class of generalized Petersen graphs was introduced by Coxeter and around 1970 popularized by Frucht, Graver and Watkins. The family of $I$-graphs mentioned in 1988 by Bouwer et al. represents a slight further albeit important generalization of the renowned Petersen graph. We show that each $I$-graph $I(n,j,k)$ admits a unit-distance representation in the Euclidean plane. This implies that each generalized Petersen graph admits a unit-distance representation in the Euclidean plane. In particular, we show that every $I$-graph $I(n,j,k)$ has an isomorphic $I$-graph that admits a unit-distance representation in the Euclidean plane with a $n$-fold rotational symmetry, with the exception of the families $I(n,j,j)$ and $I(12m,m,5m)$, $m{\geq}1$. We also provide unit-distance representations for these graphs.

• 정보처리학회논문지B
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• 제13B권2호
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• pp.83-88
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• 2006

일정한 형태의 물체를 분석하기 위해 사용되는 각-거리 그래프를 이용하여 임의의 물체의 경계선 내부 영역의 면적을 측정하는 디지털 영상처리 알고리듬을 제안한다. 물체의 경계선 내부의 한 점을 중심으로 1차 각-거리 그래프를 생성하고 이 그래프로부터 거리 값이 급격히 변화하는 위치를 추출하여 1차 그래프에서 접근하지 못한 영역을 인식하여 새 영역에서의 한 점을 중심으로 2차 각-거리 그래프를 생성한다. 물체의 형태가 복잡한 경우 차수가 증가하게 되며 이와 같이 계층적으로 구성된 각-거리 그래프 그룹에 대해 거리의 제곱을 각도 방향으로 적분하여 물체의 경계선 내부 영역의 면적을 측정한다.

• 대한수학회보
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• 제54권2호
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• pp.507-519
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• 2017

We present an upper bound on the Cheeger constant of a distance-regular graph. Recently, the authors found an upper bound on the Cheeger constant of distance-regular graph under a certain restriction in their previous work. Our new bound in the current paper is much better than the previous bound, and it is a general bound with no restriction. We point out that our bound is explicitly computable by using the valencies and the intersection matrix of a distance-regular graph. As a major tool, we use the discrete Green's function, which is defined as the inverse of ${\beta}$-Laplacian for some positive real number ${\beta}$. We present some examples of distance-regular graphs, where we compute our upper bound on their Cheeger constants.

• Journal of applied mathematics & informatics
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• 제34권3_4호
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• pp.341-354
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• 2016

In this paper, the exact formulae for the generalized product degree distance, reciprocal product degree distance and product degree distance of tensor product of a connected graph and the complete multipartite graph with partite sets of sizes m₀, m₁, ⋯ , m_r−1 are obtained.

• Kyungpook Mathematical Journal
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• 제61권1호
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• pp.61-74
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• 2021

Let G = (V, E) be a connected graph. The eccentric connectivity index of G is defined by ��C (G) = ∑u∈V (G) deg(u)e(u), where deg(u) and e(u) denote the degree and eccentricity of the vertex u in G, respectively. In this paper, we introduce a new formulation of ��C that will be called the distance eccentric connectivity index of G and defined by $${\xi}^{De}(G)\;=\;{\sum\limits_{u{\in}V(G)}}\;deg^{De}(u)e(u)$$ where degDe(u) denotes the distance eccentricity degree of the vertex u in G. The aim of this paper is to introduce and study this new topological index. The values of the eccentric connectivity index is calculated for some fundamental graph classes and also for some graph operations. Some inequalities giving upper and lower bounds for this index are obtained.

• 한국음향학회지
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• 제30권2호
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• pp.80-85
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• 2011

Speaker change detection involves the identification of time indices of an audio stream, where the identity of the speaker changes. In this paper, we propose novel measures for the speaker change detection based on a graph-partitioning criterion over the pairwise distance matrix of feature-vector stream. Experiments on both synthetic and real-world data were performed and showed that the proposed approach yield promising results compared with the conventional statistical measures.

• 한국컴퓨터정보학회논문지
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• 제24권7호
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• pp.61-69
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• 2019

In this paper, a classification method of random graph models is proposed and it is based on centralities of the random graphs. Similarity between two random graphs is measured for the classification of random graph models. The similarity between two random graph models $G^{R_1}$ and $G^{R_2}$ is defined by the distance of $G^{R_1}$ and $G^{R_2}$, where $G^{R_2}$ is a set of random graph $G^{R_2}=\{G_1^{R_2},...,G_p^{R_2}\}$ that have the same number of nodes and edges as random graph $G^{R_1}$. The distance($G^{R_1},G^{R_2}$) is obtained by comparing centralities of $G^{R_1}$ and $G^{R_2}$. Through the computational experiments, we show that it is possible to compare random graph models regardless of the number of vertices or edges of the random graphs. Also, it is possible to identify and classify the properties of the random graph models by measuring and comparing similarities between random graph models.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.421-426
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• 2007

The problem of vertex labeling with a condition at distance two in a graph, is a variation of Hale's channel assignment problem, which was first explored by Griggs and Yeh. For positive integer $p{\geq}q$, the ${\lambda}_{p,q}$-number of graph G, denoted ${\lambda}(G;p,q)$, is the smallest span among all integer labellings of V(G) such that vertices at distance two receive labels which differ by at least q and adjacent vertices receive labels which differ by at least p. Van den Heuvel and McGuinness have proved that ${\lambda}(G;p,q){\leq}(4q-2){\Delta}+10p+38q-24$ for any planar graph G with maximum degree ${\Delta}$. In this paper, we studied the upper bound of ${\lambda}_{p,q}$-number of some planar graphs. It is proved that ${\lambda}(G;p,q){\leq}(2q-1){\Delta}+2(2p-1)$ if G is an outerplanar graph and ${\lambda}(G;p,q){\leq}(2q-1){\Delta}+6p-4q-1$ if G is a Halin graph.

• 한국정보통신학회논문지
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• 제20권10호
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• pp.1967-1972
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• 2016

본 논문은 깊이 영상의 손 영역을 위해 거리 그래프를 정의하고 그것을 이용해 손가락을 검출하는 알고리즘을 제안한다. 거리 그래프는 손바닥 중심과 손 윤곽선 사이의 각과 유클리디안 거리로 손 윤곽선을 표현한 그래프이다. 거리 그래프는 손끝들의 위치에서 국부 최댓값을 갖고 있어 손가락 위치를 검출할 수 있고 손가락 개수를 인식할 수 있다. 윤곽선은 항상 360 개의 각으로 나누어지고 그들은 손목 중심을 기준으로 정렬된다. 그래서 제안된 알고리즘은 손의 크기와 방향에 대해 영향을 받지 않으며 손가락을 잘 검출한다. 다소 제한된 인식 실험 조건에서 손가락 개수 인식 실험은 1~3 개의 손가락은 100% 인식율과 4~5 개 손가락은 98% 인식율을 보여주었고, 또한 실패한 경우도 추가 가능한 단순한 조건에 의해 인식이 가능할 수 있음을 보여주었다.

• 대한수학회지
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• 제53권1호
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• pp.115-126
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• 2016

Let $E{\subset}{\mathbb{F}}^d_q$, the d-dimensional vector space over the finite field with q elements. Construct a graph, called the distance graph of E, by letting the vertices be the elements of E and connect a pair of vertices corresponding to vectors x, y 2 E by an edge if ${\parallel}x-y{\parallel}:=(x_1-y_1)^2+{\cdots}+(x_d-y_d)^2=1$. We shall prove that the non-overlapping chains of length k, with k in an appropriate range, are uniformly distributed in the sense that the number of these chains equals the statistically correct number, $1{\cdot}{\mid}E{\mid}^{k+1}q^{-k}$ plus a much smaller remainder.