Yazd University
Algebraic Structures and Their Applications
2382-9761
2423-3447
5
2
2018
11
01
On quasi-zero divisor graphs of non-commutative rings
1
13
EN
Raziyeh
Amirjan
Faculty of Mathematical sciences, Shahrood University of Technology, Shahrood, Iran.
raziyehamirjan@gmail.com
Ebrahim
Hashemi
0000-0002-8673-9556
Faculty of Mathematical sciences, Shahrood University of Technology, Shahrood, Iran.
eb_hashemi@yahoo.co
10.22034/as.2018.1214
Let $R$ be an associative ring with identity. A ring $R$ is called reversible if $ab=0$, then $ba=0$ for $a,b\in R$. <br />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
https://as.yazd.ac.ir/article_1214.html
https://as.yazd.ac.ir/article_1214_8bbae3d69383e097d245bafd1d8377d7.pdf
Yazd University
Algebraic Structures and Their Applications
2382-9761
2423-3447
5
2
2018
11
01
On permutably complemented subalgebras of finite dimensional Lie algebras
15
21
EN
Leila
Goudarzi
Department of mathematics, University of Ayatollah Alozma Boroujerdi, Boroujerd, Iran
le.goudarzi@abru.ac.ir
10.22034/as.2018.1215
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
https://as.yazd.ac.ir/article_1215.html
https://as.yazd.ac.ir/article_1215_addd86682e26e2e4e9874fe0d2069411.pdf
Yazd University
Algebraic Structures and Their Applications
2382-9761
2423-3447
5
2
2018
11
01
Spectra of some new extended corona
23
34
EN
Maliheh
Tajarrod
Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran
malihetajarrod2@gmail.com
Tahereh
Sistani
Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran
taherehsistani@gmail.com
10.22034/as.2018.1216
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
https://as.yazd.ac.ir/article_1216.html
https://as.yazd.ac.ir/article_1216_0a6cc5868240f0394988d16861c2cbc9.pdf
Yazd University
Algebraic Structures and Their Applications
2382-9761
2423-3447
5
2
2018
11
01
Finite groups admitting a connected cubic integral bi-Cayley graph
35
43
EN
Majid
Arezoomand
0000-0002-4614-6350
University of Larestan
arezoomand@lar.ac.ir
Bijan
Taeri
Department of mathematical sciences
Isfahan University of Technology
Isfahan, Iran.
b.taeri@cc.ac.ir
10.22034/as.2018.1217
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
https://as.yazd.ac.ir/article_1217.html
https://as.yazd.ac.ir/article_1217_916b135f40cc53c43df5d1406cdac745.pdf
Yazd University
Algebraic Structures and Their Applications
2382-9761
2423-3447
5
2
2018
11
01
No-homomorphism conditions for hypergraphs
45
53
EN
Samaneh
Tahmasebi
Faculty of Mathematical Sciences
Shahrood university of Technology, Shahrood, Shahrood, Iran.
samanehtahmasebi@shahroodut.ac.ir
Sadegh
Rahimi Sharbaf
Faculty of Mathematical Sciences
Shahrood university of Technology, Shahrood, Shahrood, Iran.
srahimi@shahroodut.ac.ir
10.22034/as.2018.1263
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
https://as.yazd.ac.ir/article_1263.html
https://as.yazd.ac.ir/article_1263_5837ea3e49312c8317d9598976971934.pdf
Yazd University
Algebraic Structures and Their Applications
2382-9761
2423-3447
5
2
2018
11
01
Internal Topology on MI-groups
55
78
EN
Hossein
Bagheri
Department of Mathematics, Yazd University, Yazd, Iran
bagheri@stu.yazd.ac.ir
S. Mohammad Sadegh
Modares
Department of Mathematics,
Yazd University, Yazd, Iran.
smodares@yazd.ac.ir
10.22034/as.2018.1333
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
https://as.yazd.ac.ir/article_1333.html
https://as.yazd.ac.ir/article_1333_05170bc08b6a871d90f675cf870931aa.pdf