Czechoslovak Mathematical Journal, Vol. 68, No. 3, pp. 647-656, 2018
Finite groups whose character degree graphs coincide with their prime graphs
Temha Erkoç, Utku Yilmaztürk, İsmail Ş. Güloğlu
Received October 19, 2016. First published March 2, 2018.
Abstract: In the literature, there are several graphs related to a finite group $G$. Two of them are the character degree graph, denoted by $\Delta(G)$, and the prime graph, $\Gamma(G)$. In this paper we classify all finite groups whose character degree graphs are disconnected and coincide with their prime graphs. As a corollary, we find all finite groups whose character degree graphs are square and coincide with their prime graphs.
Keywords: finite groups; character degree graph; prime graph