$4$-Regular prime graphs of nonsolvable groups
نویسندگان
1 Department of Clinical Psychology, Faculty of Humanities, University of Science and Culture, Tehran, Iran
2 Department of Clinical Psychology, Faculty of Humanities, University of Science and Culture, Tehran, Iran
doi
10.22108/ijgt.2019.112277.1490چکیده
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.
