Double domination in some graph operators

Abstract

Let $G$ be a nontrivial graph. A set $D\subseteq V(G)$ is a double dominating set of $G$ if $|N_G[v]\cap D|\geq 2$ for every vertex $v\in V(G)$, where $N_G[v]$ 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 connected graph $G$.