A Finite Power Prime Group and Some Applications for its Conjugacy Classes

Abstract

Suppose that G be a non-abelian metacyclic 2-group of positive type and ∆G be its non-commuting graph. Using the number of conjugacy classes of G , we investigate some graph properties of G . Also we give explicit formulas for the number of edges, vertices, clique number and chromatic number of G . It is shown that the graph G is weakly perfect.