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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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Start date: 2020Subject: search.filters.lcsh.Graph theory

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    Locating-hop domination in graphs
    Canoy, Sergio R., Jr; Salasalan, Jemma P. (Kyungpook National University, 2022)
    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 6= 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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    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.