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] g. We denote this graph by . In this paper, we present some graph theoretical properties of g-noncommuting graph. Specially, we investigate about its planarity and regularity, its clique number a...

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] g. we denote this graph by . in this paper, we present some graph theoretical properties of g-noncommuting graph. specially, we investigate about its planarity and regularity, its clique number a...

the noncommuting graph $nabla (g)$ of a group $g$ is asimple graph whose vertex set is the set of noncentral elements of$g$ and the edges of which are the ones connecting twononcommuting elements. we determine here, up to isomorphism, thestructure of any finite nonabeilan group $g$ whose noncommutinggraph is a split graph, that is, a graph whose vertex set can bepartitioned into two sets such t...

Let G be a finite group. For fixed element g in and given subgroup H of , the relative -noncommuting graph is simple undirected whose vertex set two vertices x y are adjacent if ∈ or [ ]≠ −1 . We denote this by Γ In paper, we obtain computing formulae for degree any characterize whether tree, star graph, lollipop complete together with some properties involving isomorphism graphs. also present ...

Let G be a finite non-abelian group. The noncommuting graph of G is denoted by ∇(G) and is defined as follows: the vertex set of ∇(G) is G \ Z(G) and two vertices x and y are adjacent if and only if xy 6= yx. Let p be a prime number. In this paper, it is proved that the almost simple group PGL(2, p) is uniquely determined by its noncommuting graph. As a consequence of our results the validity o...

Let H be a subgroup of finite non-abelian group G and g∈G. Z(H,G)={x∈H:xy=yx,∀y∈G}. We introduce the graph ΔH,Gg whose vertex set is G\Z(H,G) two distinct vertices x y are adjacent if x∈H or y∈H [x,y]≠g,g−1, where [x,y]=x−1y−1xy. In this paper, we determine whether tree among other results. also discuss about its diameter connectivity with special attention to dihedral groups.

Let G be a non-abelian group and let Z(G) be the center of G. Associate a graph ΓG (called noncommuting graph of G) with G as follows: Take G\Z(G) as the vertices of ΓG and join two distinct vertices x and y, whenever xy = yx. We want to explore how the graph theoretical properties of ΓG can effect on the group theoretical properties of G. We conjecture that if G and H are two non-abelian finit...

Let R be a finite ring and r∈R. The r-noncommuting graph of R, denoted by ΓRr, is simple undirected whose vertex set two vertices x y are adjacent if only [x,y]≠r [x,y]≠−r. In this paper, we obtain expressions for degrees show that ΓRr neither regular nor lollipop noncommutative. We characterize noncommutative rings such tree, in particular star graph. It also shown ΓR1r ΓR2ψ(r) isomorphic R1 R...