Kyungpook Mathematical Journal

  • 제62권1호
  • /
  • Pages.193-204
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  • 2022
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Locating-Hop Domination in Graphs

  • Canoy, Sergio R. Jr. (Department of Mathematics and Statistics, College of Science and Mathematics, Center for Graph Theory, Analysis, Premier Research Institute of Science and Mathematics, MSU-Iligan Institute of Technology) ;
  • Salasalan, Gemma P. (Department of Arts and Sciences, Institute of Teacher Education, Arts and Sciences, Davao del Sur State College)
  • 투고 : 2021.05.04
  • 심사 : 2021.10.07
  • 발행 : 2022.03.31
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초록

A subset S of V(G), where G is a simple undirected graph, is a hop dominating set if for each v ∈ V(G)＼S, there exists w ∈ S such that dG(v, w) = 2 and it is a locating-hop set if NG(v, 2) ∩ S ≠ NG(v, 2) ∩ S for any two distinct vertices u, v ∈ V(G)＼S. A set S ⊆ V(G) is a locating-hop dominating set if it is both a locating-hop and a hop dominating set of G. The minimum cardinality of a locating-hop dominating set of G, denoted by 𝛄lh(G), is called the locating-hop domination number of G. In this paper, we investigate some properties of this newly defined parameter. In particular, we characterize the locating-hop dominating sets in graphs under some binary operations.

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과제정보

The authors are very much grateful to the referee for the corrections and suggestions he or she made in the initial manuscript. This paper had been improved due to the additional inputs and insights the referee had given to the authors.

참고문헌

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