In any finite group G, the commutativity degree of G (denoted

by d(G)) is the probability that two randomly chosen elements of G commute.

More generally, for every n ≥ 2 the nth commutativity degree

(denoted by dn...

Let R be a non-commutative ring and let C(R) be the center of R. The non-commuting

graph ΓR of R associated to R is defined as a graph with R\\C(R) as the vertices and two

distinct vertices x and y are joined whenever xy \\not=yx. We...

Let G be a group. By using the set of automorphisms of G, we associate a simple graph to G denoted by Aut(G)(G). In this paper we study some properties of this graph.

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] ≠ ...

Suppose n is a fxed positive integer. We introduce the relative n-th non-commuting graph n

H;G, associated to the non-abelian subgroup H of group G. The vertex set is G n Cn

H;G in which Cn H;G = fx 2 G : [x; yn] = 1 and [xn; y] = 1...

In this paper we define the generalised non-commuting graph Γ(H,K) , where H and K are two subgroups of a non-abelian group G. Take (H ∪ K) \\ (CH(K) ∪ CK(H)) as the vertices of the graph and two distinct vertices x and y join, whenever x or y...

all g_i in G, h_i in H, i in {1,2 }. In this talk, we

will consider the probability that a randomly ordered n-tuples of

elements in a group G be a mutually commuting n-tuples and state

some relations between the notion...