On connected co-independent domination in the join, corona and lexicographic product of graphs

Abstract

A dominating set [Formula: see text] is called a connected co-independent dominating set of [Formula: see text], where [Formula: see text] is a finite simple undirected graph, if [Formula: see text] is a connected dominating set of [Formula: see text] and [Formula: see text] is an independent set. The minimum cardinality of such a set, denoted by [Formula: see text], is called the connected co-independent domination number of [Formula: see text]. In this paper, we study this concept and the corresponding parameter in graphs resulting from the join, corona and lexicographic product of two graphs. Specifically, we characterize the connected co-independent dominating sets in these types of graphs and determine the exact values of their connected co-independent domination numbers.