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Finite groups whose character degree graphs coincide with their prime graphs
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 3, pp. 647-656
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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.
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.
DOI : 10.21136/CMJ.2018.0553-16
Classification : 20C15
Keywords: finite groups; character degree graph; prime graph 
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Erkoç, Temha; Yilmaztürk, Utku; Güloğlu, İsmail Ş. Finite groups whose character degree graphs coincide with their prime graphs. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 3, pp. 647-656. doi: 10.21136/CMJ.2018.0553-16

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