More on independent transversal domination

Abstract

A set [Formula: see text] of vertices in a graph [Formula: see text] is called a dominating set if every vertex in [Formula: see text] is adjacent to a vertex in [Formula: see text]. Hamid defined a dominating set which intersects every maximum independent set in [Formula: see text] to be an independent transversal dominating set. The minimum cardinality of an independent transversal dominating set is called the independent transversal domination number of [Formula: see text] and is denoted by [Formula: see text]. In this paper we prove that for trees [Formula: see text], [Formula: see text] is bounded above by [Formula: see text] and characterize the extremal trees. Further, we characterize the class of all trees whose independent transversal domination number does not alter owing to the deletion of an edge.