Document Type : Ischia Group Theory 2016

**Author**

Department of Mathematics, Gebze Technical University, P.O.Box 41400, Gebze, Turkey

**Abstract**

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.

**Keywords**

**Main Subjects**

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Proceedings of the Ischia Group Theory 2016-Part III

September 2018Pages 1-6

**Receive Date:**12 December 2016**Revise Date:**04 April 2017**Accept Date:**08 April 2017**Published Online:**01 September 2018