Revisiting Domination, Hop Domination, and Global Hop Domination in Graphs
Keywords:domination, hop domination, global hop domination, complementary prism, shadow graph
A set S âŠ† V (G) is a hop dominating set of G if for each v âˆˆ V (G) \ S, there exists w âˆˆ 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 complementÂ of G. The minimum cardinality of a hop dominating (global hop dominating) set of G, denoted by Î³h(G)(resp.Î³gh(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.
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