Double domination in lexicographic product graphs

Abstract

In a graph G, a vertex dominates itself and its neighbours. A subset S ⊆ V(G) is said to be a double dominating set of G if S dominates every vertex of G at least twice. The minimum cardinality among all double dominating sets of G is the double domination number. In this article, we obtain tight bounds and closed formulas for the double domination number of lexicographic product graphs G ◦ H in terms of invariants of the factor graphs G and H.