Let g be a fixed element of a finite group G. We introduce the g-noncommuting

graph of G whose vertex set is whole elements of the group G and two vertices x,y are

adjacent whenever [x,y] ≠ g and [y,x] ≠ ...

Abstract: Let G be a finite group. In this paper we introduce the generalized conjugate graph Γc

(G,n)

which is a graph whose vertices are all the non-central subsets of G with n elements and two distinct