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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 p1 and p2 are joined by an edge if p1p2 divides some character degree ofG. 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. 2010 Mathematics Subject Classification: 20C15; 20D05; 20D60

Recognition by character degree graph and order of simple groups of order less than 6000