Locating-Hop Domination in Graphs
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A subset S of V (G), where G is a simple undirected graph, is a hop dominatingset 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 6= NG(v, 2) ∩ S for any two distinct vertices u, v ∈ V (G) \ S. Aset S ⊆ V (G) is a locating-hop dominating set if it is both a locating-hop and a hopdominating 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, weinvestigate some properties of this newly defined parameter. In particular, we characterizethe locating-hop dominating sets in graphs under some binary operations.
Abstract
A subset S of V (G), where G is a simple undirected graph, is a hop dominatingset 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 6= NG(v, 2) ∩ S for any two distinct vertices u, v ∈ V (G) \ S. Aset S ⊆ V (G) is a locating-hop dominating set if it is both a locating-hop and a hopdominating 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, weinvestigate some properties of this newly defined parameter. In particular, we characterizethe locating-hop dominating sets in graphs under some binary operations.
참고문헌 (14)
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