A New Characterization of Projective Special Linear Groups L3(p2)

Let G be a finite group. The vertex set of the prime-power graph of G is defined as V(G)=pep(G)|p∈ρ(G), where ρ(G) is the set of all prime divisors of the degrees of all irreducible characters of G and pep(G)=maxψ(1)p∣ψ∈Irr(G). It has been proved that the simple groups L3(p) can be characterized by its orders and vertex set of prime-power graphs. In this paper, we continue this topic and prove that L3(p2) can be uniquely characterized by its orders and degree prime-power graphs, where p is a prime.