Recognition by character degree graph and order of simple groups of order less than 6000
Behrooz Khosravi, Bahman Khosravi, Behnam Khosravi, Zahra Momen · Miskolc mathematical notes/Mathematical notes · 2014
Let G be a finite group.The character degree graph of G, which is denoted by .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 1 p 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.Also by an example we show that this result is not true for all simple groups.