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04. DSSC External Publications (Journals, Books, Conference Proceedings)

Permanent URI for this communityhttps://hdl.handle.net/20.500.14578/1

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Keyword: search.filters.keyword.Hop dominationSubject: search.filters.lcsh.Graphs

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    A variant of hop domination in graphs
    Canoy, Sergio R., Jr.; Salasalan, Gemma P. (New York Business Global, 2022)
    Let G be a connected graph with vertex and edge sets V (G) and E(G), respectively. A set S ⊆ V (G) is a hop dominating set of G if for each v ∈ V (G) \ S, there exists w ∈ S such that dG(v, w) = 2. A set S ⊆ V (G) is a super hop dominating set if ehpnG(v, V (G) \ S) ̸= ∅ for each v ∈ V (G) \ S, where ehpnG (v, V (G) \ S) is the set containing all the external hop private neighbors of v with respect to V (G) \ S. The minimum cardinality of a super hop dominating set of G, denoted by γ s h (G), is called the super hop domination number of G. In this paper, we investigate the concept and study it for graphs resulting from some binary operations. Specifically, we characterize the super hop dominating sets in the join, and lexicographic products of graphs, and determine bounds of the super hop domination number of each of these graphs.
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    Revisiting domination, hop domination, and global hop domination in graphs
    Salasalan, Gemma; Canoy, Sergio Jr. R. (New York Business Global, 2021)
    A set S ⊆ V (G) is a hop dominating set of G if for each v ∈ V (G) \ S, there exists w ∈ S such that dG(v, w) = 2. It is a global hop dominating set of G if it is a hop dominating set of both G and the complement G of G. The minimum cardinality of a hop dominating (global hop dominating) set of G, denoted by γh(G) (resp. γgh(G)), is called the hop domination (resp. global hop domination) number of G. In this paper, we give some realization results involving domination, hop domination, and global hop domination parameters. Also, we give a rectification of a result found in a recent paper of the authors and use this to prove some results in this paper.