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 ۳.۲۴ of [A‎. ‎Abdollahi‎, ‎S‎. ‎Akbari‎, ‎H‎. ‎R‎, ‎Maimani‎, ‎Non-commuting graph of a group‎, ‎J‎. ‎Algebra‎, ‎۲۹۸ (۲۰۰۶) ۴۶۸-۴۹۲.]‎. ‎We also prove that‎ ‎if G_۱‎, ‎G_۲‎, ‎ldots‎, ‎G_n are finite groups such that Z(G_i)=۱ for i=۱‎, ‎۲‎,‎ldots‎, ‎n‎ ‎and they are characterizable by non commuting graph‎, ‎then G_۱ times G_۲‎ times cdots times G_n is characterizable by non-commuting graph‎.

کلیدواژه ها:

non commuting graph ، Nilpotent groups ، Finite groups