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Title Locating-Hop Domination in Graphs
Posted by Sergio Jr. Canoy
Authors Canoy, Sergio Jr.; Salasalan, Gemma
Publication date 2022
Journal Kyungpook Mathematical Journal
Volume 62
Issue N/A
Pages 193-204
Abstract A subset S of V (G), where G is a simple undirected graph, is a hop dominating set if for each v in V (G) S, there exists w in S such that d(v,w) = 2 and it is a locating- hop set if the N(v; 2) cap S is not equal to N(v; 2) cap S for any two distinct vertices u and v in V (G) S. A subset S of 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 $gamma_{lh}(G)$, 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.
Index terms / Keywords locating-hop, hop domination, complement-locating, complement locating-dominating.