University of IsfahanInternational Journal of Group Theory2251-76508220190601Recognition of the simple groups $PSL_2(q)$ by character degree graph and order41462221210.22108/ijgt.2017.103226.1424ENZeinabAkhlaghiFaculty of Mathematics and Computer science, Amirkabir University of Technology (Tehran
Polytechnic), Tehran, IranMaryamKhatamiorcid.org/0000-0002-4495-8507BehroozKhosraviFaculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran
Polytechnic), 15914 Tehran, Iran0000-0002-2091-1210Journal Article20170330Let $G$ 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