• 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.

• Kyungpook Mathematical Journal
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• v.60 no.2
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• pp.349-359
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• 2020

We study perfect 2-colorings of regular graphs. In particular, we consider the 4-regular case. We obtain a characterization of perfect 2-colorings of toroidal grids.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.829-836
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• 2021

In this paper, we consider several domination parameters like perfect domination number, locating-domination number, open-locatingdomination number, etc. in the Mycielski graph M(G) of a graph G. We found upper bounds for locating-domination number of M(G) and computational formulae for perfect locating-domination number and open locating-domination number of M(G). We also showed that the perfect domination number of M(G) is at least that of G plus 1 and that for each positive integer n, there exists a graph G_n such that the perfect domination number of M(G_n) is equal to that of G_n plus n.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.329-336
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• 1998

The class of doubly chordal graphs is a subclass of chordal graphs and a superclass of strongly chordal graphs which arise in so many application areas. Many optimization problems like domination and Steiner tree are NP-complete on chordal graps but can be solved in polynomial time on doubly chordal graphs. The central to designing efficient algorithms for doulby chordal graphs is the concept of (canonical)doubly perfect elimination orderings. We present linear time algorithms to compute a (canonical) double perfect elimination ordering of a doubly chordal graph.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.661-669
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• 2021

For a simple, undirected graph G = (V, E), a perfect Roman dominating function (PRDF) f : V → {0, 1, 2} has the property that, every vertex u with f(u) = 0 is adjacent to exactly one vertex v for which f(v) = 2. The weight of a PRDF is the sum f(V) = ∑_v∈V f(v). The minimum weight of a PRDF is called the perfect Roman domination number, denoted by γ_R^P(G). Given a graph G and a positive integer k, the PRDF problem is to check whether G has a perfect Roman dominating function of weight at most k. In this paper, we first investigate the complexity of PRDF problem for some subclasses of bipartite graphs namely, star convex bipartite graphs and comb convex bipartite graphs. Then we show that PRDF problem is linear time solvable for bounded tree-width graphs, chain graphs and threshold graphs, a subclass of split graphs.

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.839-848
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• 2023

Let G be a simple undirected graph. A planar graph known as a Halin graph(HG) is characterised by having three connected and pendent vertices of a tree that are connected by an outer cycle. A subset S of V is said to be a dominating set of the graph G if each vertex u that is part of V is dominated by at least one element v that is a part of S. The domination number of a graph is denoted by the γ(G), and it corresponds to the minimum size of a dominating set. A dominating set S is called a secure dominating set if for each v ∈ V＼S there exists u ∈ S such that v is adjacent to u and S₁ = (S＼{v}) ∪ {u} is a dominating set. The minimum cardinality of a secure dominating set of G is equal to the secure domination number γ_s(G). In this article we found the secure domination number of Halin graph(HG) with perfet k-ary tree and also we determined secure domination of rooted product of special trees.

• Journal of KIISE:Computer Systems and Theory
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• v.35 no.2
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• pp.60-65
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• 2008

The matching preclusion set of a graph is a set of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. The matching preclusion number is the minimum cardinality over all matching preclusion sets. We show in this paper that, for any $m{\geq}4$, the matching preclusion numbers of both m-dimensional restricted HL-graph and recursive circulant $G(2^m,4)$ are equal to degree m of the networks, and that every minimum matching preclusion set is the set of edges incident to a single vertex.

• Proceedings of the IEEK Conference
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• 2003.07d
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• pp.1319-1322
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• 2003

We present a web document summarizer, simpler more condense than the existing ones, of a search engine. This summarizer generates summaries with a statistic-based summarization method using Clustering or MMR technique to reduce redundancy in the results, and that generates summaries using Perfect Link Graph. We compare the results with the summaries generated by human subjects. For the comparison, we use FScore. Our experimental results verify the accuracy of the summarization methods.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.10a
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• pp.250-278
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• 2004

The product rate variation problem, to be called the PRVP, is to sequence different type units that minimizes the maximum value of a deviation function between ideal and actual rates. The PRVP is an important scheduling problem that arises on mixed-model assembly lines. A surge of research has examined very interesting methods for the PRVP. We believe, however, that several issues are still open with respect to this problem. In this study, we consider convex bipartite graphs, perfect matchings, permanents and balanced sequences. The ultimate objective of this study is to show that we can provide a more efficient and in-depth procedure with a graph theoretic approach in order to solve the PRVP. To achieve this goal, we propose formal alternative proofs for some of the results stated in the previous studies, and establish several new results.

• Journal of Auto-vehicle Safety Association
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• v.8 no.2
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• pp.17-23
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• 2016

Construction of our machine "Digital Tacho Graph" toghether with development and intergrated management system information is attached under Traffic Safety Law in article submission. This machine "Digital Tach Graph" has been mandated on a priority basis. The entire machine is constructed with specialised components to collect data that can retrive basic information. To obtain the components to perfect the information to optimize the device and system.