• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.3
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• pp.65-75
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• 2007

A graph G is self-complementary (sc) if it is isomorphic to its complement. G is perfect if for all induced subgraphs H of G, the chromatic number of H (denoted ${\chi}$(H)) equals the number of vertices in the largest clique in H (denoted ${\omega}$(H)). An sc graph which is also perfect is known as sc perfect graph. A comparability graph is an undirected graph if it can be oriented into transitive directed graph. An sc comparability (scc) is clearly a subclass of sc perfect graph. In this paper we show that no two non-isomorphic scc graphs with n vertices each, (n<13) have same spectrum, and that the smallest positive integer for which there exists hyper-energetic scc graph is 13.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.12 no.3
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• pp.51-61
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• 2012

This paper suggests an algorithm that obtains Directed Graph Minimum Spanning Tree (DMST), using Prim MST algorithm which is Minimum Spanning Tree (MST) of undirected graph. At first, I suggested the Prim DMST algorithm that chooses Minimum Weight Arc(MWA) from out-going nodes from each node, considering differences between undirected graph and directed graph. Next, I proved a disadvantage of Prim DMST algorithm and Chu-Liu/Edmonds DMST (typical representative DMST) of not being able to find DMST, applying them to 3 real graphs. Last, as an algorithm that can always find DMST, an advanced Prim DMST is suggested. The Prim DMST algorithm uses a method of choosing MWA among out-going arcs of each node. On the other hand, the advanced Prim DMST algorithm uses a method of choosing a coinciding arc from the out-going and in-going arcs of each node. And if there is no coinciding arc, it chooses MWA from the out-going arcs from each node. Applying the suggested algorithm to 17 different graphs, it succeeded in finding the same DMST as that found by Chu-Liu/Edmonds DMST algorithm. Also, it does not require such a complicated calculation as that of Chu-Liu/Edmonds DMST algorithm to delete the cycle, and it takes less time for process than Prim DMST algorithm.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.13 no.1
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• pp.63-73
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• 1988

In this paper, an algorithm is proposed to evaluate the source-to-terminal reliability, the probability that a source node can communicate with a terminal node, in a probabilistic derected graph. By using Satyanaratana's factoring $theorem^{(7)}$, the original graph can be partitioned into two reduced graphs obtained by contracting and deleting the edge connected to the source node in the probabilistic directed graph. The edge removal proposed in this paper and the general series-parallel reduction can then be applied to the reduced graph. This edge reduction can be applied recursively to the reduced graphs until a source node can be connected to a terminal node by one edge. A computer program which can be applied to evaluating the source-to-terminal reliability in a complex and large network has also been developed.

• Korean Management Science Review
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• v.23 no.3
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• pp.63-75
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• 2006

There are many kinds of research on web graph, most of them are focus on the hyperlinked structure of the web graph. Well known results on the web graph are rich-get-richer phenomenon, small-world phenomenon, scale-free network, etc. In this paper, we define 3 new directed web graph, so called the Web Usage Pattern Graph (WUPG), that nodes represent web sites arid arcs between nodes represent a movement between two sites by users' browsing behavior. The data to constructing the WUPG, approximately 56,000 records, are gathered from some users' PCs. The results analysing the data summarized as follows : (i) extremely rich-get-richer phenomenon (ii) average path length between sites is significantly less than the previous one (iii) less external hyperlinks, more internal hyperlinks.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.9 no.1
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• pp.89-94
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• 2009

This paper proposes the algorithms that design the highly digital logic circuit and assign the code to each node of DCG(Directed Cyclic Graph) of length ${\zeta}$. The conventional algorithm have some problems, so this paper introduce the matrix equation from DCG of length ${\zeta}$ and proposes highly digital logic circuit design algorithms according to the DCG of length ${\zeta}$. Using the proposed circuit design algorithms in this paper, it become realized that was able to design from former algorithm. Also, making a comparison between the circuit using former algorithm and this paper's, we testify that proposed paper's algorithm is able to realize more optimized circuit design. According to proposed circuit design algorithm in this paper, it is possible to design current that DCG have natural number, so it have the following advantages, reduction of the circuit input/output digits, simplification of circuit composition, reduction of computation time and cost. And we show comparability and verification about this paper's algorithm.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.10a
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• pp.422-440
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• 2005

There are many kinds of research on web graph, most of them are focus on the hyperlinked structure of the web graph. Well known results on the web graph are rich-get-richer phenomenon, small-world phenomenon, scale-free network, etc. In this paper, we define a new directed web graph, so called the Web Usage Pattern Graph (WUPG), that nodes represent web sites and arcs between nodes represent a movement between two sites by users' browsing behavior. The data to constructing the WUPG, approximately 56,000 records, are gathered in the Kyungsung University. The results analysing the data summarized as follows: (i) extremely rich-get-richer phenomenon (ii) average path length between sites is significantly less than the previous one (iii) less external hyperlinks, more internal hyperlinks

• The Transactions of the Korea Information Processing Society
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• v.5 no.10
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• pp.2615-2626
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• 1998

In this paper, we propose a new interconnection network called RFM graph, whichis the merger of the directed rotator and Faber-Moore graph, and analyze fault tolerance, routing algorithm node disjoint cycles and broadcasting algorithm. We also describe methods to embed star graph, 2 dimesional torus and bubblesort graph into RFM graph with unit expasion and dilation 2.

• Proceedings of the Korea Information Processing Society Conference
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• 2000.04a
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• pp.815-820
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• 2000

Variable Reference Graph 는 C 언어로 작성된 프로그램으로부터 상호 절차적인 자료 흐름 분석 정보를 수평적 방향 그래프(directed graph)로 자동 생성해주는 역공학(reverse engineering) 도구들 중 하나이다. 본 논문에서는 판독성 있는 구조적 정보를 제공하기위한 그래픽 표현의 전략을 바탕으로 JAVA 로 구현된 그래픽 사용자 인터페이스(graphic user interface) 및 그래프 레이아웃 알고리즘(graph layout algorithm)을 기술한다. 이 알고리즘은 4 단계로 구성되어 있다: 정보 모형, 레벨 알고리즘, 순서 알고리즘, 위치 알고리즘. 각 단계별에서 수행되는 주요 알고리즘을 살펴 본다. 특히, 이 알고리즘들은 사이클(cycle) 및 비사이클(acyclic) 방향 그래프, 그리고 트리(tree)를 수평적 계층 구조를 생성하는데 사용될 수 있다. 본 논문에서 구현된 Variable Reference Graph 는 소프트웨어 재공학 도구를 개발하는 RESORT(RESearch on object-oriented SOftware Reengineering Technology) 과제에서 개발되었다.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.651-661
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• 2007

Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies an identity $s{\approx}t$ if the corresponding graph algebra $\underline{A(G)}$ satisfies $s{\approx}t$. A graph G=(V,E) is called an $(xy)x{\approx}x(yy)$ graph if the graph algebra $\underline{A(G)}$ satisfies the equation $(xy)x{\approx}x(yy)$. An identity $s{\approx}t$ of terms s and t of any type ${\tau}$ is called a hyperidentity of an algebra $\underline{A}$ if whenever the operation symbols occurring in s and t are replaced by any term operations of $\underline{A}$ of the appropriate arity, the resulting identities hold in $\underline{A}$. In this paper we characterize $(xy)x{\approx}x(yy)$ graph algebras, identities and hyperidentities in $(xy)x{\approx}x(yy)$ graph algebras.

• Journal of the Korean Institute of Telematics and Electronics
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• v.22 no.1
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• pp.28-33
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• 1985

A modified directed product graph (DPGm) is proposed for the numerator of the network functions of a given non-reciprocal network. By this, the numerator can be obtained topologically and systematically without the sign rule of the Mason's formula and without the change of topological prcperties of the net work throughout the processes. And by taking the subgraph of the DPGm for each vertex, a number of cancelling terms can be removed mechanically from the DPGm beforehand and there(ore the above can be acquired more simply and rapidly.