# Institute of Mathematics

## 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
Classification MSC:  20C15
DOI:  10.21136/CMJ.2018.0553-16

PDF available at:  Institute of Mathematics CAS

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Affiliations:   Temha Erkoç, Utku Yilmaztürk, Department of Mathematics, Faculty of Science, Istanbul University, Vezneciler, 34134 Fatih, Istanbul, Turkey, e-mail: erkoctemha@gmail.com, uyilmazturk@gmail.com; İsmail Ş. Güloğlu, Department of Mathematics, Doğuş University, Hasanpasa Mah., Zeamet Sok. No: 21, 34722 Acibadem, Istanbul, Turkey, e-mail: iguloglu@dogus.edu.tr

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