University of Isfahan International Journal of Group Theory 2251-7650 8 2 2019 06 01 Recognition of the simple groups $PSL_2(q)$ by character degree graph and order 41 46 22212 10.22108/ijgt.2017.103226.1424 EN Zeinab Akhlaghi Faculty of Mathematics and Computer science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran Maryam Khatami Behrooz Khosravi Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 15914 Tehran, Iran Journal Article 2017 03 30 ‎‎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 $G\cong PSL_2(q)$‎. https://ijgt.ui.ac.ir/article_22212_c6dca60b79cceb6b7922abee8ca0c87c.pdf