A set S of vertices in a graph G is a neighbourhood set of G if G = where is the subgraph of G induced by v and all points adjacent to v. A neighbourhood set S V of a graph G is said to be an independent transversal neighbourhood, if S intersects every maximum independent set of G. The minimum cardinality of an independent transversal neighbourhod set of G is called the independent transversal neighbourhood number of G and is denoted by ηit(G). In this paper we begin an investigation of this parameter.
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