Recognition of the simple groups PSL2(q) by character degree graph and order

Let g be a finite group‎, ‎and irr(g) be the set of complex irreducible characters of g‎. ‎let ρ(g) be the set of prime divisors of character degrees of g‎. ‎the character degree graph of g‎, ‎which is denoted by δ(g)‎, ‎is a simple graph with vertex set ρ(g)‎, ‎and we join two vertices r and s by an edge if there exists a character degree of g divisible by rs‎. ‎in this paper‎, ‎we prove that if g is a finite group such that δ(g)=δ( psl2(q)) and |g|=| psl2(q)|‎, ‎then g≅ psl2(q)‎.