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 ...

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 group. By using a family َA of subsets of automorphisms of G, we introduced a simple graph T_A(G), which is a generalization of the non-commuting graph. In this paper, we study the combinatorial properties of T_A(G)....

Abstract In this paper, we introduce the new concept isoclinism of two non-commuting graphs. We describe it with this hope to determine the properties of the graph with large number of vertices and edges more easier by use of its smaller...

Let $G$ be a non-abelian group and $H$ a subgroup of $G$. We associate a graph $\\Gamma_{(G,H)}$ to $H$ and $G$ as follows: Take $G_C_G(H)$ as the vertices of $\\Gamma_{(G,H)}$ and join two distinct vertices $x$ and $y$, ...

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...

Let G be a finite non-abelian group and g a fixed element of G. In 2014, Tolue et al. introduced the g-noncommuting graph of G, which was denoted by Γg G with vertex set G and two distinct vertices x and y join by an edge ...

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...

For any group G and any fixed element g of G, we may as-

sociate a graph is denoted by g

G as an undirected graph whose vertices

are all elements of G and two distinct vertices x and y are adjacent ...