Open-independent dominating sets in lexicographic product of graphs

Abstract

An open-independent dominating set (OIND-set) S for a graph G is a set of vertices where no vertex in S has more than one neighbor within S, and every vertex in G is dominated by S. The minimum cardinality of an OIND-set is denoted by γoind(G). This work presents results concerning the γoind(G) of the lexicographic product G ◦ H. Specifically, we establish exact values under specific constraints on G, and provide bounds relative to another domination variant, as well as γoind(G) and γoind(H) .