4-Regular prime graphs of nonsolvable groups

Abstract

Let G be a finite group and cd(G) denote the character degree set for G. The prime graph ∆(G) is a simple graph whose vertex set consists of prime divisors of elements in cd(G), denoted ρ(G). Two primes p, q ∈ ρ(G) are adjacent in ∆(G) if and only if pq|a for some a ∈ cd(G). We determine which simple 4-regular graphs occur as prime graphs for some finite nonsolvable group.