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)....

Let R be a ring with the identity element 1, α be an endomorphism of R and b be a

left α-derivation. In this paper, we introduce a generalization of a commuting graph,

which is denoted by ΓR(α, b), as a directed graph with vertex set R...

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...

The commuting graph of a group G, denoted by \\\\\\\\Gamma(G), is a simple graph whose vertices are all non-central elements of G and two distinct vertices x,y are adjacent if xy=yx....

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 ...