@article { author = {Amirjan, Raziyeh and Hashemi, Ebrahim}, title = {On quasi-zero divisor graphs of non-commutative rings}, journal = {Algebraic Structures and Their Applications}, volume = {5}, number = {2}, pages = {1-13}, year = {2018}, publisher = {Yazd University}, issn = {2382-9761}, eissn = {2423-3447}, doi = {10.22034/as.2018.1214}, abstract = {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 $\Gamma(R[x])$.}, keywords = {quasi-zero-divisor graph,zero-divisor graph,reversible ring,reduced ring,diameter}, url = {https://as.yazd.ac.ir/article_1214.html}, eprint = {https://as.yazd.ac.ir/article_1214_8bbae3d69383e097d245bafd1d8377d7.pdf} } @article { author = {Goudarzi, Leila}, title = {On permutably complemented subalgebras of finite dimensional Lie algebras}, journal = {Algebraic Structures and Their Applications}, volume = {5}, number = {2}, pages = {15-21}, year = {2018}, publisher = {Yazd University}, issn = {2382-9761}, eissn = {2423-3447}, doi = {10.22034/as.2018.1215}, abstract = {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.}, keywords = {Lie algebra,permutably complemented,completely factorisable,solvable,supersolvable}, url = {https://as.yazd.ac.ir/article_1215.html}, eprint = {https://as.yazd.ac.ir/article_1215_addd86682e26e2e4e9874fe0d2069411.pdf} } @article { author = {Tajarrod, Maliheh and Sistani, Tahereh}, title = {Spectra of some new extended corona}, journal = {Algebraic Structures and Their Applications}, volume = {5}, number = {2}, pages = {23-34}, year = {2018}, publisher = {Yazd University}, issn = {2382-9761}, eissn = {2423-3447}, doi = {10.22034/as.2018.1216}, abstract = {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.}, keywords = {spectrum,corona,neighborhood corona,integral graphs}, url = {https://as.yazd.ac.ir/article_1216.html}, eprint = {https://as.yazd.ac.ir/article_1216_0a6cc5868240f0394988d16861c2cbc9.pdf} } @article { author = {Arezoomand, Majid and Taeri, Bijan}, title = {Finite groups admitting a connected cubic integral bi-Cayley graph}, journal = {Algebraic Structures and Their Applications}, volume = {5}, number = {2}, pages = {35-43}, year = {2018}, publisher = {Yazd University}, issn = {2382-9761}, eissn = {2423-3447}, doi = {10.22034/as.2018.1217}, abstract = {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.}, keywords = {Bi-Cayley graph,Integer eigenvalues,Irreducible representation}, url = {https://as.yazd.ac.ir/article_1217.html}, eprint = {https://as.yazd.ac.ir/article_1217_916b135f40cc53c43df5d1406cdac745.pdf} } @article { author = {Tahmasebi, Samaneh and Rahimi Sharbaf, Sadegh}, title = {No-homomorphism conditions for hypergraphs}, journal = {Algebraic Structures and Their Applications}, volume = {5}, number = {2}, pages = {45-53}, year = {2018}, publisher = {Yazd University}, issn = {2382-9761}, eissn = {2423-3447}, doi = {10.22034/as.2018.1263}, abstract = {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.}, keywords = {hypergraph homomorphism,independing number,Clique number,chromatic number,fractional chromatic number}, url = {https://as.yazd.ac.ir/article_1263.html}, eprint = {https://as.yazd.ac.ir/article_1263_5837ea3e49312c8317d9598976971934.pdf} } @article { author = {Bagheri, Hossein and Modares, S. Mohammad Sadegh}, title = {Internal Topology on MI-groups}, journal = {Algebraic Structures and Their Applications}, volume = {5}, number = {2}, pages = {55-78}, year = {2018}, publisher = {Yazd University}, issn = {2382-9761}, eissn = {2423-3447}, doi = {10.22034/as.2018.1333}, abstract = {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.}, keywords = {MI-groups,Monoid,Pseudoidentity elements,canonical MI-subgroup,Full MI-subgroup,Internal topology}, url = {https://as.yazd.ac.ir/article_1333.html}, eprint = {https://as.yazd.ac.ir/article_1333_05170bc08b6a871d90f675cf870931aa.pdf} }