A Characterization of L_4(4) by Its Noncommuting Graph

Let G be a nonabelian group and associate a noncommuting graph▽(G) with G as follows:The vertex set of▽(G) is G\Z(G) with two vertices x and y joined by an edge whenever the commutator of x and y is not the identity.In 2006,Abdollahi A.,Akbari S.and Maimani H. R.put forward a conjecture called AAM's Conjecture as follows:If M is a finite nonabelian simple group and G is a group such that▽(G)≌▽(M),then G≌M.Even though this conjecture is known to hold for all simple groups with nonconnected prime graphs and the alternating group A_(10), it is still unknown for all simple groups with connected prime graphs except A_(10).It is proved that the conjecture is also true for the projective special linear simple group L_4(4).