Independent transversal domination in graphs

A set S ⊆ 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. A dominating set which intersects every maximum independent set in G is called 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 ${\displaystyle {\gamma }_{it}\left(G\right)}$. In this paper we begin an investigation of this parameter.