University of IsfahanInternational Journal of Group Theory2251-76509320200901$4$-Regular prime graphs of nonsolvable groups1932222371810.22108/ijgt.2019.112277.1490ENDonnieKasyokiSchool of Mathematics, Statistics and Actuarial Science, Maseno University,
KenyaPaulOlecheDepartment of Pure and Mathematics, Maseno University, P.O. Box 333, Maseno, KenyaJournal Article20180727Let $G$ 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.https://ijgt.ui.ac.ir/article_23718_69ca905b94960ef358bf148a4b31e12a.pdf