Some Results on Divisibility Graph in Some Classes of Finite Groups

A nite group G is called an F????group, if for every x; y 2 G n Z(G), CG(x) CG(y) implies that CG(x) = CG(y). The graph D(G) is called the divisibility graph of G if its vertex set is the non-central conjugacy class sizes of G and there is an edge between vertices a and b if and only if ajb or bja. We determine the number of connected components of the divisibility graph D(G) where G is an F????group.