Finite groups whose character degree graphs 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 I"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