some results on characterization of finite group by non commuting graph

the non commuting graph 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 [2]. we also prove that if $g_1$, $g_2$, ..., $g_n$ are finite groups such that $z(g_i)=1$ for $i=1,2,...,n$ and they are characterizable by non commuting graph, then $g_1times ...times g_n$ is characterizable by non commuting graph.