University of Isfahan International Journal of Group Theory 2251-7650 7 3 2018 09 01 On nonsolvable groups whose prime degree graphs have four vertices and one triangle 1 6 21476 10.22108/ijgt.2017.21476 EN Roghayeh Hafezieh Department of‎ ‎Mathematics‎, ‎Gebze Technical University‎, ‎P.O.Box 41400, Gebze‎, ‎Turkey Journal Article 2016 12 12 ‎Let $G$ 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