• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.337-344
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• 1997

In this paper, we study the isomorphism problem of Cayley permutation graphs. We obtain a necessary and sufficient condition that two Cayley permutation graphs are isomrphic by a direction-preserving and color-preserving (positive/negative) natural isomorphism. The result says that if a graph G is the Cayley graph for a group $\Gamma$ then the number of direction-preserving and color-preserving positive natural isomorphism classes of Cayley permutation graphs of G is the number of double cosets of $\Gamma^\ell$ in $S_\Gamma$, where $S_\Gamma$ is the group of permutations on the elements of $\Gamma and \Gamma^\ell$ is the group of left translations by the elements of $\Gamma$. We obtain the number of the isomorphism classes by counting the double cosets.

• Annals of Fuzzy Mathematics and Informatics
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• v.16 no.3
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• pp.363-371
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• 2018

The main objective of this paper is to connect fuzzy theory, graph theory and fuzzy graph theory with algebraic structure. We introduce the notion of fuzzy graph of semigroup, the notion of fuzzy ideal graph of semigroup as a generalization of fuzzy ideal of semigroup, intuitionistic fuzzy ideal of semigroup, fuzzy graph and graph, the notion of isomorphism of fuzzy graphs of semigroups and regular fuzzy graph of semigroup and we study some of their properties.

• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.175-184
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• 2002

A Cellular embedding of a graph G into an orientable surface S can be considered as a cellular decomposition of S into 0-cells, 1-cells and 2-cells and vise versa, in which 0-cells and 1-cells form a graph G and this decomposition of S is called a map in S with underlying graph G. For a map M with underlying graph G, we define a natural rotation on the line graph of the graph G and we introduce the line map for M. we find that genus of the supporting surface of the line map for a map and we give a characterization for the line map to be embedded in the sphere. Moreover we show that the line map for any life of a map M is map-isomorphic to a lift of the line map for M.

• Journal of the Korea Society of Computer and Information
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• v.21 no.12
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• pp.1-10
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• 2016

In this paper, we attempt to prevent certain cases by tracing a history and making genogram about open source software and its modification using similarity of source code. There are many areas which use open source software actively and widely, and open source software contributes their development. However, there are many unconscious cases like ignoring license or intellectual properties infringe which can lead litigation. To prevent such situation, we analyze source code similarity using program dependence graph which resembles subgraph isomorphism problem, a typical NP-complete problem. To solve subgraph isomorphism problem, we utilized harmony search of metaheuristic algorithm and compared its result with a genetic algorithm. For the future works, we represent open source software as program dependence graph and analyze their similarity.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.831-837
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• 1995

In this paper, we introduce a permutation graph over a graph G as a generalization of both a graph bundle over G and a standard permutation graph, and study a characterization of a natural isomorphism and an automorphism of permutation graphs over a graph.

• Proceedings of the Korean Society for Bioinformatics Conference
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• 2005.09a
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• pp.267-271
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• 2005

The goal of data mining is to extract new and useful knowledge from large scale datasets. As the amount of available data grows explosively, it became vitally important to develop faster data mining algorithms for various types of data. Recently, an interest in developing data mining algorithms that operate on graphs has been increased. Especially, mining frequent patterns from structured data such as graphs has been concerned by many research groups. A graph is a highly adaptable representation scheme that used in many domains including chemistry, bioinformatics and physics. For example, the chemical structure of a given substance can be modelled by an undirected labelled graph in which each node corresponds to an atom and each edge corresponds to a chemical bond between atoms. Internet can also be modelled as a directed graph in which each node corresponds to an web site and each edge corresponds to a hypertext link between web sites. Notably in bioinformatics area, various kinds of newly discovered data such as gene regulation networks or protein interaction networks could be modelled as graphs. There have been a number of attempts to find useful knowledge from these graph structured data. One of the most powerful analysis tool for graph structured data is frequent subgraph analysis. Recurring patterns in graph data can provide incomparable insights into that graph data. However, to find recurring subgraphs is extremely expensive in computational side. At the core of the problem, there are two computationally challenging problems. 1) Subgraph isomorphism and 2) Enumeration of subgraphs. Problems related to the former are subgraph isomorphism problem (Is graph A contains graph B?) and graph isomorphism problem(Are two graphs A and B the same or not?). Even these simplified versions of the subgraph mining problem are known to be NP-complete or Polymorphism-complete and no polynomial time algorithm has been existed so far. The later is also a difficult problem. We should generate all of 2$^n$ subgraphs if there is no constraint where n is the number of vertices of the input graph. In order to find frequent subgraphs from larger graph database, it is essential to give appropriate constraint to the subgraphs to find. Most of the current approaches are focus on the frequencies of a subgraph: the higher the frequency of a graph is, the more attentions should be given to that graph. Recently, several algorithms which use level by level approaches to find frequent subgraphs have been developed. Some of the recently emerging applications suggest that other constraints such as connectivity also could be useful in mining subgraphs : more strongly connected parts of a graph are more informative. If we restrict the set of subgraphs to mine to more strongly connected parts, its computational complexity could be decreased significantly. In this paper, we present an efficient algorithm to mine frequent subgraphs that are more strongly connected. Experimental study shows that the algorithm is scaling to larger graphs which have more than ten thousand vertices.

• Journal of IKEEE
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• v.3 no.2 s.5
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• pp.295-304
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• 1999

This paper presents a method of constructing the Multiple-Valued Logic Systems(MVLS) over Finite Fields(FF) using by Decision Diagram(DD) that is based on Graph Theory. The proposed method is as following. First, we derivate the Ordered Multiple-Valued Logic Decision Diagram(OMVLDD) based on the multiple-valued Shannon's expansion theorem and we execute function decomposition using by sub-graph. Next, we propose the variable selecting algorithm and simplification algorithm after apply the each isomorphism and reodering vertex. Also we propose MVLS design method.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1169-1183
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• 2015

We describe generalized Cayley graphs of rectangular groups, so that we obtain (1) an equivalent condition for two Cayley graphs of a rectangular group to be isomorphic to each other, (2) a necessary and sufficient condition for a generalized Cayley graph of a rectangular group to be (strong) connected, (3) a necessary and sufficient condition for the colour-preserving automorphism group of such a graph to be vertex-transitive, and (4) a sufficient condition for the automorphism group of such a graph to be vertex-transitive.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.1145-1153
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• 2023

The notion of maximal product of two fuzzy graphs was introduced by Radha and Arumugam in 2015 and the notion of balanced fuzzy graph was introduced by Al-Hawary in 2011. In this paper, we give a modification of the maximal product definition, which we call maximal strong product. We also introduce the relatively new notion of maximal-balanced fuzzy graphs. We give necessary and sufficient conditions for the maximal strong product of two balanced (resp., maximal-balanced) fuzzy graphs to be balanced (resp., maximal-balanced) and we prove that these two independent notions are preserved under isomorphism.

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.301-307
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• 2017

In this paper, we solve the following four graph equations $L^k(G)=H{\oplus}J$; $M(G)=H{\oplus}J$; ${\bar{L^k(G)}}=H{\oplus}J$ and ${\bar{M(G)}}=H{\oplus}J$, where J is $nK_2$ for $n{\geq}1$. Here, the equality symbol = means the isomorphism between the corresponding graphs. In particular, we shall obtain all pairs of graphs (G, H), which satisfy the above mentioned equations, upto isomorphism.