Abstract
Let G be a finite group. The degree (vertex) graph Γ(G) attached to G is a character degree graph. Its vertices are the degrees of the nonlinear irreducible complex characters of G, and different vertices m, n are adjacent if the greatest common divisor (m, n) > 1. In this paper, we classify all graphs with four vertices that occur as Γ(G) for nonsolvable groups G.
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