Journal of applied mathematics & informatics

  • 제41권4호
  • /
  • Pages.839-848
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  • 2023
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  • 2734-1194(pISSN)
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  • 2234-8417(eISSN)
한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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SECURE DOMINATION PARAMETERS OF HALIN GRAPH WITH PERFECT K-ARY TREE

  • R. ARASU (Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology) ;
  • N. PARVATHI (Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology)
  • 투고 : 2022.11.10
  • 심사 : 2023.03.13
  • 발행 : 2023.07.30
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초록

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 γs(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.

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과제정보

We would like to thank the unknown referees for their comments and suggestions on the manuscript in improving from an earlier version. The authors R. Arasu and N. Parvathi are very much thankful to the management, SRM Institute of Science and Technology for their continuous support and encouragement.

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