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

A dominating set D ⊆ V (G) is called a connected co-independent dominating set of G , where G is a finite simple undirected graph, if D is a connected dominating set of G and V (G) ∖ D is an independent set. The minimum cardinality of such a set, denoted by γ c , coi (G) , is called the connected co-independent domination number of G. 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. [ABSTRACT FROM AUTHOR]