Some results on characterization of finite group by non commuting graph

The non commuting graph nabla(g) of a non-abelian finite group g is defined as follows: its vertex set is g - z(g) and two distinct vertices x and y are joined by an edge if and only if the commutator of x and y is not the identity. in this paper we prove some new results about this graph. in particular we will give a new proof of theorem 3.24 of [a. abdollahi, s. akbari, h. r, maimani, non-commuting graph of a group, j. algebra, 298 (2006) 468-492.]. we also prove that if g1;g2; : : : ;gn are nite groups such that z(gi) = 1 for i = 1; 2; : : : ; n and they are characterizable by non commuting graph, then g1 * g2 * . . . * gn is characterizable by non-commuting graph