Diameters of degree graphs of nonsolvable groups, II

Let G be a finite group and let cd(G) be the set of irreducible character degrees of G. The degree graph Δ(G) is the graph whose set of vertices is the set of primes that divide degrees in cd(G), with an edge between p and q if pq divides a for some degree a cd(G). It is shown using the degree graphs of the finite simple groups that if G is a nonsolvable group, then the diameter of Δ(G) is at most 3.