Degree graphs of simple orthogonal and symplectic groups

Let G be a finite group and let cd(G) be the set of irreducible ordinary character degrees of G. The degree graph of G is the graph Δ(G) whose set of vertices is the set of primes dividing degrees in cd(G), with an edge between primes p1 and p2 if p1p2 divides some degree in cd(G). We determine the graph Δ(G) for the finite simple groups of types Bℓ, Cℓ, Dℓ and ; that is, for the simple orthogonal and symplectic groups.