Character degree graphs of solvable groups with diameter three

Let G be a finite solvable group and cd(G) the set of character degrees of G. The character degree graph Delta(G) is the graph whose vertices are the primes dividing the degrees in cd(G) and there is an edge between two distinct primes p and q if their product pq divides some degree in cd(G). When Delta(G) has diameter three, we can partition the vertices rho(G) into four non-empty disjoint subsets rho(1) boolean OR rho(2) boolean OR rho(3) boolean OR rho(4) where no prime in rho(1) is adjacent to any prime in rho(3) boolean OR rho(4); no prime in rho(4) is adjacent to any prime in rho(1) boolean OR rho(2); every prime in rho(2) is adjacent to some prime in rho(3); every prime in rho(3) is adjacent to some prime in rho(2); and vertical bar rho(1) boolean OR rho(2)vertical bar <= vertical bar rho(3) boolean OR rho(4)vertical bar. We will show the following: If G is a solvable group where Delta(G) has diameter three, then rho(3) has at least three vertices and G has a normal non-abelian Sylow p-subgroup where p is an element of rho(3). If rho(1) boolean OR rho(2) has n vertices, then rho(3) boolean OR rho(4) must have at least 2(n) vertices. The group G has Fitting height 3.