Document Type: Research Paper
Faculty of Mathematics and Computer science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 15914 Tehran, Iran
Let $G$ be a finite group, and $\Irr(G)$ be the set of complex irreducible characters of $G$. Let $\rho(G)$ be the set of prime divisors of character degrees of $G$. The character degree graph of $G$, which is denoted by $\Delta(G)$, is a simple graph with vertex set $\rho(G)$, 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 $\Delta(G)=\Delta(\PSL_2(q))$ and $|G|=|\PSL_2(q)|$, then $G\cong\PSL_2(q)$.