The total co-independent domination number of some graph operations

Abstract

. A set D of vertices of a graph G is a total dominating set if every vertex of G is adjacent to at least one vertex of D . The total domi- nating set D is called a total co-independent dominating set if the subgraph induced by V ( G ) − D is edgeless. The minimum cardinality among all total co-independent dominating sets of G is the total co-independent domination number of G . In this article we study the total co-independent domination number of the join, strong, lexicographic, direct and rooted products of graphs.