Let G be a finite group and cd(G) denote the character degree set for G. The prime graph Δ(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 Δ(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.
@article{arxiv.1901.03492,
title = {4-Regular prime graphs of nonsolvable groups},
author = {Donnie Munyao Kasyoki and Paul Odhiambo Oleche},
journal= {arXiv preprint arXiv:1901.03492},
year = {2019}
}