‎$‎4‎$‎-Regular prime graphs of nonsolvable groups

Document Type : Research Paper


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


Let $G$ be a finite group and $\cd(G)$ denote the character degree set for $G$. The prime graph $\DG$ 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 $\DG$ 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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