• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.415-430
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• 2018

A proper vertex coloring of a graph G is acyclic if G contains no bicolored cycle. A graph G is acyclically L-list colorable if for a given list assignment $L=\{L(v):v{\in}V(G)\}$, there exists an acyclic coloring ${\phi}$ of G such that ${\phi}(v){\in}L(v)$ for all $v{\in}V(G)$ A graph G is acyclically k-choosable if G is acyclically L-list colorable for any list assignment with $L(v){\geq}k$ for all $v{\in}V(G)$. Let G be a planar graph without 5-cycles and adjacent 4-cycles. In this article, we prove that G is acyclically 5-choosable if every vertex v in G is incident with at most one i-cycle, $i {\in}\{6,7\}$.

• Journal of the Korean Mathematical Society
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• v.46 no.2
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• pp.313-325
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• 2009

We consider zero-divisor graphs with respect to primal, nonprimal, weakly prime and weakly primal ideals of a commutative ring R with non-zero identity. We investigate the interplay between the ringtheoretic properties of R and the graph-theoretic properties of ${\Gamma}_I(R)$ for some ideal I of R. Also we show that the zero-divisor graph with respect to primal ideals commutes by localization.

• Proceedings of the Korea Information Processing Society Conference
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• 2023.05a
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• pp.386-388
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• 2023

본 논문은 고성능 스토리지를 사용하는 환경에서 대규모 그래프를 분석을 위한 GPU 기반 그래프 분석 엔진의 I/O 최적화 전략을 제안한다. 사전 실험을 통해 최신 GPU 기반 그래프 엔진인 RealGraph^GPU 가 고성능 스토리지의 대역폭을 충분히 활용하지 못하고 있음을 발견하였다. 이를 개선하기 위해 (1) User-space I/O, (2) Asynchronous I/O 두 가지 최적화 전략을 적용하였으며, 실험을 통해 두 전략이 RealGraphGPU 의 그래프 분석 성능 향상시키는 데 효과적임을 확인하였다.

• Journal of the Korea Society of Computer and Information
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• v.20 no.7
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• pp.41-47
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• 2015

The bandwidth minimization problem (BMP) has been classified as NP-complete because the polynomial time algorithm to find the optimal solution has been unknown yet. This paper suggests polynomial time heuristic algorithm is to find the solution of bandwidth minimization problem. To find the minimum bandwidth ${\phi}^*=_{min}{\phi}(G)$, ${\phi}(G)=_{max}\{{\mid}f(v_i)-f(v_j):v_i,v_j{\in}E\}$ for given graph G=(V,E), m=|V|,n=|E|, the proposed algorithm sets the maximum degree vertex $v_i$ in graph G into global central point (GCP), and labels the median value ${\lceil}m+1/2{\rceil}$ between [1,m] range. The graph G is partitioned into subgroup, the maximum degree vertex in each subgroup is set to local central point (LCP), and we adjust the label of LCP per each subgroup as possible as minimum distance from GCP. The proposed algorithm requires O(mn) time complexity for label to all of vertices. For various twelve graph, the proposed algorithm can be obtains the same result as known optimal solution. For one graph, the proposed algorithm can be improve on known solution.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.27-43
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• 2022

The one-sided fattenings (called semi-ribbon graph in this paper) of the graph embedded in the real projective plane ℝℙ² are completely classified up to topological equivalence. A planar graph (i.e., embedded in the plane), admitting the one-sided fattening, is known to be a cactus boundary. For the graphs embedded in ℝℙ² admitting the one-sided fattening, unlike the planar graphs, a new building block appears: a bracelet along the Möbius band, which is not a connected summand of the oriented surfaces.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.2
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• pp.9-14
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• 2007

A signed 3-partite graph is a 3-partite graph in which each edge is assigned a positive or a negative sign. Let G(U, V, W) be a signed 3-partite graph with $U\;=\;\{u_1,\;u_2,\;{\cdots},\;u_p\},\;V\;=\;\{v_1,\;v_2,\;{\cdots},\;v_q\}\;and\;W\;=\;\{w_1,\;w_2,\;{\cdots},\;w_r\}$. Then, signed degree of $u_i(v_j\;and\;w_k)$ is $sdeg(u_i)\;=\;d_i\;=\;d^+_i\;-\;d^-_i,\;1\;{\leq}\;i\;{\leq}\;p\;(sdeg(v_j)\;=\;e_j\;=\;e^+_j\;-\;e^-_j,\;1\;{\leq}\;j\;{\leq}q$ and $sdeg(w_k)\;=\;f_k\;=\;f^+_k\;-\;f^-_k,\;1\;{\leq}\;k\;{\leq}\;r)$ where $d^+_i(e^+_j\;and\;f^+_k)$ is the number of positive edges incident with $u_i(v_j\;and\;w_k)$ and $d^-_i(e^-_j\;and\;f^-_k)$ is the number of negative edges incident with $u_i(v_j\;and\;w_k)$. The sequences ${\alpha}\;=\;[d_1,\;d_2,\;{\cdots},\;d_p],\;{\beta}\;=\;[e_1,\;e_2,\;{\cdots},\;e_q]$ and ${\gamma}\;=\;[f_1,\;f_2,\;{\cdots},\;f_r]$ are called the signed degree sequences of G(U, V, W). In this paper, we characterize the signed degree sequences of signed 3-partite graphs.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.20 no.2
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• pp.415-420
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• 2016

A graph G=(V,E) is called an interval graph with a set V of vertices representing intervals on a line such that there is an edge $(i,j){\in}E$ if and only if intervals i and j intersect. In this paper, we are concerned in the vertex connectivity, one of various characteristics of the graph. Specifically, the vertex connectivity of an interval graph is represented by the overlapping of intervals. Also we propose an efficient algorithm to compute the vertex connectivity on the fully dynamic environment in which the vertices or the edges are inserted or deleted. Using a special kind of interval tree, we show how to compute the vertex connectivity and to maintain the tree in O(logn) time when a new interval is added or an existing interval is deleted.

• Journal of applied mathematics & informatics
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• v.38 no.3_4
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• pp.221-238
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• 2020

Let G = (V (G), E(G)) be a graph and let g : V (G) → S₃ be a function. For each edge xy assign the label r where r is the remainder when o(g(x)) is divided by o(g(y)) or o(g(y)) is divided by o(g(x)) according as o(g(x)) ≥ o(g(y)) or o(g(y)) ≥ o(g(x)). The function g is called a group S₃ cordial remainder labeling of G if |v_g(i)-v_g(j)| ≤ 1 and |e_g(1)-e_g(0)| ≤ 1, where v_g(j) denotes the number of vertices labeled with j and e_g(i) denotes the number of edges labeled with i (i = 0, 1). A graph G which admits a group S₃ cordial remainder labeling is called a group S₃ cordial remainder graph. In this paper, we prove that subdivision of graphs admit a group S₃ cordial remainder labeling.

• Journal of the Korean School Mathematics Society
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• v.13 no.2
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• pp.289-301
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• 2010

This study discovered that instructional objectives of graphs which are dealt with in Math I of the revised curriculum are not matched with those of Discrete Mathematics in the 7th Curriculum. Based on the findings, this study analysed didactic transposition method of trail in graph and matrix of Math I and students' understanding about trail. Then this study discovered that though the concept definition of trail in Math I of the revised curriculum, some textbooks and students tend to consider it as the path. The concept definition of trail is significant in systems that deal with Euler Circuits(Euler Closed trail) and Hamilton Cycle. Then it is not easy to find the value of trail in Math I of the revised curriculum.

• Journal for History of Mathematics
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• v.23 no.4
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• pp.83-100
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• 2010

This paper is to raise several questions in teaching the Graph and Linear Transformation complied with the Mathematics Amended Curriculum announced in 2006 Aug. and then to formulate a plan accordingly. For this, we'll take a good look at the prior studies on the Graph and Linear Transformation after the announcement of the 7th School Curriculum along with the changes in their contents through the process of curriculum. Then we'll check over learning factors of the Graph and Linear Transformation in all 27 kinds of the authorized textbooks - 'Mathematics I', 'Applications of Mathematics', and 'Geometry and Vectors' - and 27 kinds of exercise books issued on 2009. By this, we put measures which improve understanding and apply correctly to the Graph and Linear Transformation in the Mathematics Amended Curriculum to high school teachers.