Let G be a nite group. Then a simple graph associated to group G denoted by G is called the non-commuting graph of G whose vertex set V ( G) is G n Z(G) and the edge set E( G) is the set of all fx; yg, where x and y are distinct elements in G n Z(G) such that [x; y] = x 1y 1xy = 1. In this talk, we introduce some dierent graphs which are generalizations of non-commuting graph of G. They obtain by dierent views and ideas of generalization, for instance by associating to a subgroup H of G or assuming n th power of elements of G or corresponding to an automorphism and so on. We will introduce ve types of such graphs which are all a generalization of non-commuting graph of G. We present the general information and basic properties about these graphs which are mostly new or a generalization of some properties on non-commuting graph G given by Abdollahi et al. in 2006.

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