A Graph Related to Conjugacy Classes of Solvable Groups Original Research Article

Let G be a finite group and Γ*(G) a graph whose vertices are the prime divisors of conjugacy classes sizes of G, and two vertices are connected if they both divide the size of some conjugacy class of G. The main purpose of this paper is to prove that if G is solvable and does not involve a certain special subgroup of the semi-linear group, then Γ*(G) is composed of two complete subgraphs.