• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.89-100
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• 2015

In this paper, we present exact formulae for the multiplicatively weighted Harary indices of join, tensor product and strong product of graphs in terms of other graph invariants including the Harary index, Zagreb indices and Zagreb coindices. Finally, We apply our result to compute the multiplicatively weighted Harary indices of fan graph, wheel graph and closed fence graph.

• Journal of the Korean Operations Research and Management Science Society
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• v.14 no.1
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• pp.27-35
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• 1989

An algorithm that searches the general AND-OR graph is proposed. The convergence and the efficiency of the algorithm is examined and compared with an existing algorithm for the AND-OR graph. It is proved that the proposed algorithm is superior to the existing method both in the quality of the solution and the number of node expansions.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.05a
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• pp.718-721
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• 2004

This paper introduces a novel method of partitioning a cyclic workflow graph into the subgraphs of acyclic flows. The way of iterative classification of nodes according to feedback structures and deriving subgraphs of acyclic flows is described with illustrative examples. The proposed method allows a cyclic workflow model to be analyzed further, if necessary, with several smaller subflows, which are all acyclic.

• 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

• Journal of the Korea Institute of Information and Communication Engineering
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• v.6 no.5
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• pp.653-660
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• 2002

This paper proposes a method for storing graphs and defining graph algorithms based on the well-developed relational database. In this method, graphs are represented in the form of relations. Each vertex and edge of a graph is represented as tuples of the table and saved in a database. We developed a library of graph operations for the storage and management of graphs and the development of graph applications. Furthermore, we defined graph algorithms in terms of relational algebraic operations such as projection, selection, and join. They can be implemented with the database language such as SQL. This database approach provides an efficient methodology to deal with very large-scale graphs and to support the development of graph applications.

• Journal of the Korean Operations Research and Management Science Society
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• v.21 no.1
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• pp.131-146
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• 1996

In this paper, we describe the facial structure of the steiner problem in a directed graph by formulating it as set covering problem. We first characterize trivial facets and derive a necessary condition for nontrival facets. We also introduce a class of valid inequalities with 0-1 coefficients and show when such inequalities define facets.

• Journal of the Korean Operations Research and Management Science Society
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• v.28 no.4
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• pp.131-143
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• 2003

In this paper, we present a survey about the various graph partition problems including the clustering problem, the k-cut problem, the multiterminal cut problem, the multicut problem, the sparsest cut problem, the network attack problem, the network disconnection problem. We compare those problems focusing on the problem characteristics such as the objective function and the conditions that the partitioned clusters should satisfy. We also introduce the mathematical programming formulations, and the solution approaches developed for the problems.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.545-557
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• 2015

A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we define two new operation on vague graphs namely normal product and tensor product and study about the degree of a vertex in vague graphs which are obtained from two given vague graphs G₁ and G₂ using the operations cartesian product, composition, tensor product and normal product. These operations are highly utilized by computer science, geometry, algebra, number theory and operation research. In addition to the existing operations these properties will also be helpful to study large vague graph as a combination of small, vague graphs and to derive its properties from those of the smaller ones.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.10a
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• pp.161-164
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• 2000

A cyclic shop is a production system that repeatedly produces identical sets of jobs, called minimal part sets, in the same loading and processing sequence. We consider a version of cyclic shop where the operations are processed and unloaded within time limits, so called a time window. We model the shop using an event graph model, a class of Petri nets. To represent the time window constraint, we introduce places with negative time delays. From the shop modeling graph, we develop a linear system model based on the max- plus algebra and characterize the conditions on the existence of a stable schedule.

• Journal of KIISE:Databases
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• v.29 no.5
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• pp.347-357
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• 2002

Graphs have provided a powerful methodology to solve a lot of real-world problems, and therefore there have been many proposals on the graph representations and algorithms. But, because most of them considered only memory-based graphs, there are still difficulties to apply them to large-scale problems. To cope with the difficulties, this paper proposes a graph representation and graph algorithms based on the well-developed relational database theory. Graphs are represented in the form of relations which can be visualized as relational tables. Each vertex and edge of a graph is represented as a tuple in the tables. Graph algorithms are also defined in terms of relational algebraic operations such as projection, selection, and join. They can be implemented with the database language such as SQL. We also developed a library of basic graph operations for the management of graphs and the development of graph applications. This database approach provides an efficient methodology to deal with very large- scale graphs, and the graph library supports the development of graph applications. Furthermore, it has many advantages such as the concurrent graph sharing among users by virtue of the capability of database.