2024-03-29T06:09:03Z
https://as.yazd.ac.ir/?_action=export&rf=summon&issue=251
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2018
5
2
On quasi-zero divisor graphs of non-commutative rings
Raziyeh
Amirjan
Ebrahim
Hashemi
Let $R$ be an associative ring with identity. A ring $R$ is called reversible if $ab=0$, then $ba=0$ for $a,b\in R$. The quasi-zero-divisor graph of $R$, denoted by $\Gamma^*(R)$ is an undirected graph with all nonzero zero-divisors of $R$ as vertex set and two distinct vertices $x$ and $y$ are adjacent if and only if there exists $0\neq r\in R \setminus (\mathrm{ann}(x) \cup \mathrm{ann}(y))$ such that $xry=0$ or $yrx=0$. In this paper, we determine the diameter and girth of $\Gamma^*(R)$. We show that the zero-divisor graph of $R$ denoted by $\Gamma(R)$, is an induced subgraph of $\Gamma^*(R)$. Also, we investigate when $\Gamma^*(R)$ is identical to $\Gamma(R)$. Moreover, for a reversible ring $R$, we study the diameter and girth of $\Gamma^*(R[x])$ and we investigate when $\Gamma^*(R[x])$ is identical to $\Gamma(R[x])$.
quasi-zero-divisor graph
zero-divisor graph
reversible ring
reduced ring
diameter
2018
11
01
1
13
https://as.yazd.ac.ir/article_1214_8bbae3d69383e097d245bafd1d8377d7.pdf
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2018
5
2
On permutably complemented subalgebras of finite dimensional Lie algebras
Leila
Goudarzi
Let $L$ be a finite-dimensional Lie algebra. We say a subalgebra $H$ of $L$ is permutably complemented in $L$ if there is a subalgebra $K$ of $L$ such that $L=H+K$ and $H\cap K=0$. Also, if every subalgebra of $L$ is permutably complemented in $L$, then $L$ is called completely factorisable. In this article, we consider the influence of these concepts on the structure of a Lie algebra, in particular, we obtain some characterizations for supersolvability of a finite-dimensional Lie algebra in terms of permutably complemented subalgebras.
Lie algebra
permutably complemented
completely factorisable
solvable
supersolvable
2018
11
01
15
21
https://as.yazd.ac.ir/article_1215_addd86682e26e2e4e9874fe0d2069411.pdf
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2018
5
2
Spectra of some new extended corona
Maliheh
Tajarrod
Tahereh
Sistani
For two graphs $\mathrm{G}$ and $\mathrm{H}$ with $n$ and $m$ vertices, the corona $\mathrm{G}\circ\mathrm{H}$ of $\mathrm{G}$ and $\mathrm{H}$ is the graph obtained by taking one copy of $\mathrm{G}$ and $n$ copies of $\mathrm{H}$ and then joining the $i^{th}$ vertex of $\mathrm{G}$ to every vertex in the $i^{th}$ copy of $\mathrm{H}$. The neighborhood corona $\mathrm{G}\star\mathrm{H}$ of $\mathrm{G}$ and $\mathrm{H}$ is the graph obtained by taking one copy of $\mathrm{G}$ and $n$ copies of $\mathrm{H}$ and joining every neighbor of the $i^{th}$ vertex of $\mathrm{G}$ to every vertex in the $i^{th}$ copy of $\mathrm{H}$. In this paper, we define four new extensions of corona and neighborhood corona of two graphs $\mathrm{G}$ and $\mathrm{H}$; named the identity-extended corona, identity-extended neighborhood corona, neighborhood extended corona and neighborhood extended neighborhood corona and then determine the spectrum of their adjacency matrix, where $\mathrm{H}$ is a regular graph. As an application, we exhibit infinite families of integral graphs.
spectrum
corona
neighborhood corona
integral graphs
2018
11
01
23
34
https://as.yazd.ac.ir/article_1216_0a6cc5868240f0394988d16861c2cbc9.pdf
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2018
5
2
Finite groups admitting a connected cubic integral bi-Cayley graph
Majid
Arezoomand
Bijan
Taeri
A graph is called integral if all eigenvalues of its adjacency matrix are integers. Given a subset $S$ of a finite group $G$, the bi-Cayley graph $BCay(G,S)$ is a graph with vertex set $G\times\{1,2\}$ and edge set $\{\{(x,1),(sx,2)\}\mid s\in S, x\in G\}$. In this paper, we classify all finite groups admitting a connected cubic integral bi-Cayley graph.
Bi-Cayley graph
Integer eigenvalues
Irreducible representation
2018
11
01
35
43
https://as.yazd.ac.ir/article_1217_916b135f40cc53c43df5d1406cdac745.pdf
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2018
5
2
No-homomorphism conditions for hypergraphs
Samaneh
Tahmasebi
Sadegh
Rahimi Sharbaf
In this paper, we define some new homomorphism-monotone parameters for hypergraphs. Using these parameters, we extend some graph homomorphism results to hypergraph case. Also, we present some bounds for some well-known invariants of hypergraphs such as fractional chromatic number,independent numer and some other invariants of hyergraphs, in terms of these parameters.
hypergraph homomorphism
independing number
Clique number
chromatic number
fractional chromatic number
2018
11
01
45
53
https://as.yazd.ac.ir/article_1263_5837ea3e49312c8317d9598976971934.pdf
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2018
5
2
Internal Topology on MI-groups
Hossein
Bagheri
S. Mohammad Sadegh
Modares
An MI-group is an algebraic structure based on a generalization of the concept of a monoid that satisfies the cancellation laws and is endowed with an invertible anti-automorphism representing inversion. In this paper, a topology is defined on an MI-group $G$ under which $G$ is a topological MI-group. Then we will identify open, discrete and compact MI-subgroups. The connected components of the elements of $G$ and connected MI-groups are also identified. Some features of the maximal MI-subgroups and ideals of a topological MI-group are investigated as well. Finally, some theorems about automatic continuity will be introduced.
MI-groups
Monoid
Pseudoidentity elements
canonical MI-subgroup
Full MI-subgroup
Internal topology
2018
11
01
55
78
https://as.yazd.ac.ir/article_1333_05170bc08b6a871d90f675cf870931aa.pdf