Independent transversal domination subdivision number of trees

A set S subset of V of vertices in a graph G = ( V, E ) is called a dominating set if every vertex in V \ S is adjacent to a vertex in S. The domination number (gamma )( G ) is the minimum cardinality of a dominating set of G . The domination subdivision number sd (gamma) ( G ) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the domination number. Sahul Hamid defined a dominating set which intersects every maximum independent set in G to be an independent transversal dominating set. The minimum cardinality of an independent transversal dominating set is called the independent transversal domination number of G and is denoted by (gamma) (it) ( G ). We extend the idea of domination subdivision number to independent transversal domination. The independent transversal domination subdivision number of a graph G denoted by sd (gamma it )( G ) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the independent transversal domination number. In this paper we initiate a study of this parameter with respect to trees.