Double domination in some graph operators

Abstract

Let G be a nontrivial graph. A set D ⊆ V(G) is a double dominating set of G if | \mathrm{N_G} [v] ∩ D| ≥ 2 for every vertex v ∈ V(G), where \mathrm{N_G} [v] represents the closed neighborhood of v. The double domination number of G is the minimum cardinality among all double dominating sets of G. In this paper we study this domination parameter in some well-known graph operators defined from a onnected graph G.