  Given a finite group G, let cd(G) denote the set of degrees of the
irreducible complex characters of G. The character degree graph of G is defined
as the simple undirected graph whose vertices are the prime divisors of the
numbers in cd(G), two distinct vertices p and q being adjacent if and only if
pq divides some number in cd(G). In this paper, we consider the complement of
the character degree graph, and we characterize the finite groups for which
this complement graph is not bipartite. This extends the analysis of [1], where
the solvable case was treated.

Group Theory