Recognition by noncommuting graph of finite simple groups L 4(q)

Let G be a nonabelian group. We define the noncommuting graph a double dagger(G) of G as follows: its vertex set is G\Z(G), the set of non-central elements of G, and two different vertices x and y are joined by an edge if and only if x and y do not commute as elements of G, i.e., [x, y] not equal 1. We prove that if L a {L (4)(7), L (4)(11), L (4)(13), L (4)(16), L (4)(17)} and G is a finite group such that a double dagger(G) a parts per thousand... a double dagger(L), then G a parts per thousand... L.