• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권3호
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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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• 제60권2호
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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.

• 대한수학회보
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• 제58권4호
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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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• 제5권2호
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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.

• Journal of applied mathematics & informatics
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• 제42권3호
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• pp.625-634
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• 2024

The thrust of this paper is to extend the notion of Plithogenic vertex domination to the basic operations in Plithogenic product fuzzy graphs (PPFGs). When the graph is a complete PPFG, Plithogenic vertex domination numbers (PVDNs) of its Plithogenic complement and perfect Plithogenic complement are the same, since the connectivities are the same in both the graphs. Since extra edges are added to the graph in the case of perfect Plithogenic complement, the PVDN of perfect Plithogenic complement is always less than or equal to that of Plithogenic complement, when the graph under consideration is an incomplete PPFG. The maximum and minimum values of the PVDN of the intersection or the union of PPFGs depend upon the attribute values given to P-vertices, the number of attribute values and the connectivities in the corresponding PPFGs. The novelty in this study is the investigation of the variations and the relations between PVDNs in the operations of Plithogenic complement, perfect Plithogenic complement, union and intersection of PPFGs.

• Kyungpook Mathematical Journal
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• 제61권3호
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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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• 제41권4호
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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.

• 한국정보과학회논문지:시스템및이론
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• 제35권2호
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• pp.60-65
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• 2008

그래프의 매칭 배제 집합은 그것을 삭제한 그래프가 완전 매칭이나 준완전 매칭을 가지지 않는 에지 집합이다. 매칭 배제수는 모든 매칭 배제 집합의 최소 크기이다. 이 논문에서는 임의의 $m{\geq}4$에 대하여 H-차원 제한된 HL-그래프와 재귀원형군 $G(2^m,4)$의 매칭 배제수는 분지수 m과 같고, 모든 최소 매칭 배제 집합은 한 정점에 인접한 에지 집합임을 보인다.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2003년도 하계종합학술대회 논문집 Ⅲ
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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.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 2004년도 추계학술대회 및 정기총회
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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.