Global Hop Domination Numbers of Graphs

Abstract

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 d_G(v, w) = 2. It is a global hop dominating set of G if it is a hop dominatingset of both G and the complement of G. The minimum cardinality of a global hop dominatingset of G, denoted by γ_gh(G), is called the global hop domination number of G. In this paper, we study the concept of global hop domination in graphs resulting from some binary operations.