The Divisibility Graph for F-Groups.

A graph is called the divisibility graph of if its vertex set is the set of noncentral conjugacy class sizes of and there is an edge between vertices and if and only if or . We determine the number of connected components of the divisibility graph when is an F-group. A finite group is called an F-group if for every , implies . We also prove that if the divisibility graph in which is an F-group is a -regular graph, then the divisibility graph is a complete graph with vertices. [ABSTRACT FROM AUTHOR]