• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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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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• v.30 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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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.

• Journal of Korea Multimedia Society
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• v.6 no.4
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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.

• Journal of the Korean Mathematical Society
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• v.49 no.6
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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 $p$.

• KIISE Transactions on Computing Practices
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• v.24 no.1
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• pp.40-45
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• 2018

With the advent of big data and social networks, large-scale graph processing becomes popular research topic. Recently, an optimization technique called Gorder has been proposed to improve the performance of in-memory graph processing. This technique improves performance by optimizing the graph layout on memory to have better cache locality. However, since it is designed for in-memory graph processing systems, the technique is not suitable for disk-based graph engines; also the cost for applying the technique is significantly high. To solve the problem, we propose a new graph ordering called I/O Order. I/O Order considers the characteristics of I/O accesses for SSDs and HDDs to improve the performance of disk-based graph engine. In addition, the algorithmic complexity of I/O Order is simple compared to Gorder, hence it is cheaper to apply I/O Ordering. I/O order reduces the cost of pre-processing up to 9.6 times compared to that of Gorder's, still its performance is 2 times higher compared to the Random in low-locality graph algorithms.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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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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• v.30 no.1_2
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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.

• Journal of Korea Multimedia Society
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• v.5 no.3
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• pp.331-341
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• 2002

Traditional slicing techniques make slices through dependence graph and 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. We propose the representation of a dynamic system dependence graph so as to process the slicing of a software system that is composed of related programs in order to process certain jobs. We also propose programs on efficient slicing algorithm using relations of relative tables in order to compute dynamic slices of a software system. Using a marking table from results of the proposed algorithm can make dynamic system dependence graph for dynamic slice generation. Tracing this graph can generate final slices. We have illustrated our example with C program environment. Consequently, the efficiency of the proposed dynamic system dependence graph technique is also compared with the dependence graph techniques discussed previously. As the results, this is certifying that the dynamic system dependence graph is more efficient in comparison with system dependence graph.

• Proceedings of the Korea Society for Industrial Systems Conference
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• 2008.10b
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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.