Hop Dominating Sets in Graphs Under Binary Operations

Sergio Canoy, Jr, Reynaldo Villarobe Mollejon, John Gabriel E. Canoy


Let G be a (simple) 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. The minimum cardinality of a hop dominating set of G, denoted by γh(G), is called the hop domination number of G. In this paper we revisit the concept of hop domination, relate it with other domination concepts, and investigate it in graphs resulting from some binary operations.


domination, hop domination, join, corona, and lexicographic product

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