In this paper, we calculate diameters of connected components of commuting graphs of GLn(S), for an integer n ≥ 2 and a commutative antinegative entire semiring S, unless n is a non-prime odd number and S has at least two invertible elements.

The commuting graph ∆(G) of a group G is the graph whose vertex set is the group and two distinct elements x and y being adjacent if and only if xy = yx. In this paper the automorphism group of this graph is investigated. We observe that Aut(∆(G)) is a non-abelian group such that its order is not prime power and square-free.

In this paper, diameters of connected components of commuting graphs of GLn(S) are calculated, for an integer n ≥ 2 and a commutative antinegative entire semiring S, unless n is a non-prime odd number and S has at least two invertible elements.

The non-commuting graph $Gamma(G)$ of a non-abelian group $G$ with the center $Z(G)$ is a graph with thevertex set $V(Gamma(G))=Gsetminus Z(G)$ and two distinct vertices $x$ and $y$ are adjacent in $Gamma(G)$if and only if $xy neq yx$. The aim of this paper is to compute the spectra of some well-known NC-graphs.

Let $G$ be a non-abelian group and let $Z(G)$ be the center of $G$. Associate with $G$ there is agraph $Gamma_G$ as follows: Take $Gsetminus Z(G)$ as vertices of$Gamma_G$ and joint two distinct vertices $x$ and $y$ whenever$yxneq yx$. $Gamma_G$ is called the non-commuting graph of $G$. In recent years many interesting works have been done in non-commutative graph of groups. Computing the clique...

Let G be a finite non-abelian group and denote by Z(G) its center. The non-commuting graph of on transversal the center is whose vertices are non-central elements in two x y adjacent whenever xy=yx. In this work, we classify groups centeris double-toroidal or 1-planar.

The paper is in two parts. In Part I we describe a construction of a certain kind of subdirect product of a family of rings. We endow the index set of the family with the partial order structure of an SFP domain, as introduced by Plotkin, and provide a commuting system of homomorphisms between those rings whose indices are related in the ordering. We then take the subdirect product consisting o...

A flexible unified framework for both classical and quantum Schubert calculus is proposed. It is based on a natural combinatorial approach relying on the Hasse-Schmidt extension of a certain family of pairwise commuting endomorphisms of an infinite free Z-module M to its exterior algebra M .

For any finite Coxeter system (W,S) we construct a certain noncommutative algebra, the so-called bracket algebra, together with a family of commuting elements, the so-called Dunkl elements. The Dunkl elements conjecturally generate an algebra which is canonically isomorphic to the coinvariant algebra of the Coxeter group W. We prove this conjecture for classical Coxeter groups and I2(m). We def...