• 대한수학회보
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• 제59권1호
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• pp.203-212
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• 2022

A simple graph is called semi-symmetric if it is regular and edge transitive but not vertex transitive. In this paper we prove that there is no connected cubic semi-symmetric graph of order 12p³ for any prime number p.

• Korean Journal of Mathematics
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• 제30권2호
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• pp.391-402
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• 2022

For a given graph G = (V, E), a dominating set is a subset V' of the vertex set V so that each vertex in V ＼ V' is adjacent to a vertex in V'. The minimum cardinality of a dominating set of G is called the domination number of G and is denoted by γ(G). For an integer k ≥ 1, the k-th power G^k of a graph G with V (G^k) = V (G) for which uv ∈ E(G^k) if and only if 1 ≤ d_G(u, v) ≤ k. Note that G² is the square graph of a graph G. In this paper, we obtain some tight bounds for the sum of the domination numbers of a graph and its square graph in terms of the order, order and size, and maximum degree of the graph G. Also, we characterize such extremal graphs.

• 대한수학회보
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• 제55권6호
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• pp.1667-1690
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• 2018

We consider the minimum order of a graph G with a given lazy cop number $c_L(G)$. Sullivan, Townsend and Werzanski [7] showed that the minimum order of a connected graph with lazy cop number 3 is 9 and $k_3{\square}k_3$ is the unique graph on nine vertices which requires three lazy cops. They conjectured that for a graph G on n vertices with ${\Delta}(G){\geq}n-k^2$, $c_L(G){\leq}k$. We proved that the conjecture is true for k = 4. Furthermore, we showed that the Petersen graph is the unique connected graph G on 10 vertices with ${\Delta}(G){\leq}3$ having lazy cop number 3 and the minimum order of a connected graph with lazy cop number 4 is 16.

• 한국멀티미디어학회논문지
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• 제6권4호
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• pp.736-745
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• 2003

Traditional slicing techniques make slices through dependence graphs. They also improve the accuracy of slices. However, traditional slicing techniques require many vertices and edges in order to express a data communication link because they are based on static slicing techniques. Therefore the graph becomes very complicated, and size of the slices is larger. We propose the representation of a dynamic object-oriented program dependence graph so as to process the slicing of object-oriented programs that is composed of related programs in order to process certain jobs. We also propose an efficient slicing algorithm using the relations of relative tables in order to compute dynamic slices of object-oriented programs. Consequently, the efficiency of the proposed efficient dynamic object-oriented program dependence graph technique is also compared with the dependence graph techniques discussed previously As a result, this is certifying that an efficient dynamic object-oriented program dependence graph is more efficient in comparison with the traditional object-oriented dependence graphs and dynamic object-oriented program dependence graph.

• 대한수학회지
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• 제49권6호
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• pp.1111-1121
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• 2012

A graph is symmetric if its automorphism group acts transitively on the set of arcs of the graph. In this paper, we classify tetravalent symmetric graphs of order $9p$ for each prime $p$.

• 정보과학회 컴퓨팅의 실제 논문지
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• 제24권1호
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• pp.40-45
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• 2018

빅데이터와 소셜 네트워크의 발전과 더불어 거대한 그래프를 처리하는 연구도 활발하게 진행되고 있다. 최근 그래프 처리의 성능 향상을 위해 Gorder 라는 그래프 오더링 기법이 제안되었다. 이 기법은 메모리 상의 그래프 레이아웃을 변형하여 데이터 접근 패턴을 CPU 캐시에 적합하게 바꿈으로써 성능을 향상시킨다. 하지만 그래프 알고리즘의 캐시 지역성에만 초점을 두고 설계되었기 때문에 디스크 기반 그래프 엔진에서는 적합하지 않고 전처리 비용도 크다는 문제점이 있다. 제시한 문제점을 해결하기 위해, 본 논문에서는 새로운 그래프 오더링인 I/O Order를 제안하였다. I/O Order는 디스크 기반의 그래프 엔진에서 지역성 외에 입출력 부하를 고려하여 설계되었다. 또한, 오더링 비용을 줄이기 위해 간단한 scheme을 사용한다. 본 논문에서 제시된 I/O Order는 Gorder와 비교해 전처리 비용이 최대 9.6배 감소하였고 성능은 지역성이 낮은 그래프 알고리즘에서 Random 대비 최대 2배 이상 향상되었다.

• 대한수학회보
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• 제57권3호
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• pp.739-750
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• 2020

A simple graph is called semisymmetric if it is regular and edge transitive but not vertex transitive. Let p be a prime. Folkman proved [J. Folkman, Regular line-symmetric graphs, Journal of Combinatorial Theory 3 (1967), no. 3, 215-232] that no semisymmetric graph of order 2p or 2p² exists. In this paper an extension of his result in the case of cubic graphs of order 34p³, p ≠ 17, is obtained.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.245-252
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• 2012

In this paper we present a necessary and sufficient conditions for an infinite VAP-free plane graph to be a 3LV-graph as well as an LV-graph. We also introduce and investigate the concept of the order and the kernel of an infinite connected graph containing no one-way infinite path.

• 한국멀티미디어학회논문지
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• 제5권3호
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• pp.331-341
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• 2002

기존의 슬라이싱 기법들은 슬라이스를 생성하며 생성된 슬라이스의 정확성을 위해 종속 그래프를 사용한다. 그러나, 기존의 많은 슬라이싱 기법들은 동적 슬라이싱 기법에 바탕을 두고 데이터 통신 링크를 표현하기 때문에 많은 정점들(vertices)과 간선들(edges)을 필요로 한다. 그러므로 그 그래프는 매우 복잡하다. 어떤 프로그램 시스템에 대한 소프트웨 어 슬라이싱을 처리하기 위해 본 논문에서는 동적 시스템 종속그래프를 제안한다. 그리고, 소프트웨어 시스템의 동적 슬라이스를 산출하기 위해 관련 테이블들의 관계도를 이용한 효율적인 슬라이싱 알고리즘을 제안한다. 동적 슬라이스의 생성을 위한 동적시스템종속그래프는 제안된 알고리즘으로부터 얻어진 마킹테이블을 사용해서 얻어진다. 슬라이스의 최종 결과는 이 그래프를 추적함으로써 얻어진다. 결론적으로 제안된 동적시스템종속그래프 기법의 효율성을 기존의 종속그래프 기법과 비교하였다.

• 한국산업정보학회:학술대회논문집
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• 한국산업정보학회 2008년도 추계 공동 국제학술대회
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• pp.651-655
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• 2008

Traditional slicing techniques make slices through dependence graphs. They also improve the accuracy of slices. However, traditional slicing techniques require many vertices and edges in order to express a data communication links. Therefore the graph becomes complicated, and size of the slices is larger. We propose the representation of a dynamic object-oriented program dependence graph so as to process the slicing of object-oriented programs that is composed of related programs in order to process certain jobs. The efficiency of the proposed efficient dynamic object-oriented program dependence graph technique is also compared with the dependence graph techniques discussed previously. As a result, this is certifying that an efficient dynamic object-oriented program dependence graph is more efficient in comparison with the traditional dynamic object-oriented program dependence graph.