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http://dx.doi.org/10.5666/KMJ.2022.62.1.193

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)
Publication Information
Kyungpook Mathematical Journal / v.62, no.1, 2022 , pp. 193-204 More about this Journal
Abstract
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.
Keywords
locating-hop; hop domination; complement-locating; complement locating-dominating;
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