Groups whose Bipartite Divisor Graph for Character Degrees Has Five Vertices.

Let G be a finite group and cd-(G) be the set of nonlinear irreducible character degrees of G. Suppose that -(G) denotes the set of primes dividing some element of cd-(G). The bipartite divisor graph for the set of character degrees which is denoted by B(G), is a bipartite graph whose vertices are the disjoint union of -(G) and cd-(G), and a vertex p 2 -(G) is connected to a vertex a 2 cd-(G) if and only if p|a. In this paper, we investigate the structure of a group G whose graph B(G) has five vertices. Especially we show that all these groups are solvable. [ABSTRACT FROM AUTHOR]