University of IsfahanInternational Journal of Group Theory2251-76507320180901On nonsolvable groups whose prime degree graphs have four vertices and one triangle162147610.22108/ijgt.2017.21476ENRoghayehHafeziehDepartment of Mathematics, Gebze Technical University, P.O.Box 41400, Gebze, TurkeyJournal Article20161212Let $G$ be a finite group. The prime degree graph of $G$, denoted by $Delta(G)$, is an undirected graph whose vertex set is $rho(G)$ and there is an edge between two distinct primes $p$ and $q$ if and only if $pq$ divides some irreducible character degree of $G$. In general, it seems that the prime graphs contain many edges and thus they should have many triangles, so one of the cases that would be interesting is to consider those finite groups whose prime degree graphs have a small number of triangles. In this paper we consider the case where for a nonsolvable group $G$, $Delta(G)$ is a connected graph which has only one triangle and four vertices.https://ijgt.ui.ac.ir/article_21476_7aa9bd067cc2235a1faa46dd8f4728af.pdf