%0 Journal Article
%T $4$-Regular prime graphs of nonsolvable groups
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A Kasyoki, Donnie
%A Oleche, Paul
%D 2020
%\ 09/01/2020
%V 9
%N 3
%P 193-222
%! $4$-Regular prime graphs of nonsolvable groups
%K Nonsolvable group
%K character
%K character degree
%K graph
%K prime graph
%R 10.22108/ijgt.2019.112277.1490
%X 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.
%U https://ijgt.ui.ac.ir/article_23718_69ca905b94960ef358bf148a4b31e12a.pdf