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Keywords:
finite groups; character degree graph; prime graph
Summary:
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.
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