‎$‎4‎$‎-Regular prime graphs of nonsolvable groups

Document Type : Research Paper

Authors

1 School of Mathematics, Statistics and Actuarial Science, Maseno University, Kenya

2 Department of Pure and‎ ‎Mathematics‎, ‎Maseno University‎, ‎P.O‎. ‎Box 333, Maseno‎, ‎Kenya

Abstract

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 $\rho(G)$. Two primes $p,q\in \rho(G)$ are adjacent in $Δ(G)$ if and only if $pq|a$ for some $a\in cd(G)$. We determine which simple $4$-regular graphs occur as prime graphs for some finite nonsolvable group.

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International Journal of Group Theory
Volume 9, Issue 3 - Serial Number 3
September 2020
Pages 193-222

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