independent transversal domination subdivision number of trees

A set $ssubseteq v $ of vertices in a graph $g=(v,e)$ is called a dominating set if every vertex in $v setminus 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 textit{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.