MMN-777
Recognition by character degree graph and order of simple groups of order less than 6000
Abstract
Let $G$ be a finite group. The character degree graph of $G$, which is denoted by $\Gamma(G)$, is the graph whose vertices are the prime divisors of the character degrees of the group $G$ and two vertices $p_1$ and $p_2$ are joined by an edge if $p_1p_2$ divides some character degree of $G$. In this paper we prove that if $G$ is a simple group of order less that 6000, then $G$ is uniquely determined by its character degree graph and its order.
Vol. 15 (2014), No. 2, pp. 537-544