Yazd UniversityAlgebraic Structures and Their Applications2382-97615220181101On quasi-zero divisor graphs of non-commutative rings113121410.22034/as.2018.1214ENRaziyehAmirjanFaculty of Mathematical sciences, Shahrood University of Technology, Shahrood, Iran.EbrahimHashemiFaculty of Mathematical sciences, Shahrood University of Technology, Shahrood, Iran.0000-0002-8673-9556Journal Article20180714Let $R$ 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 $\Gamma(R[x])$.https://as.yazd.ac.ir/article_1214_8bbae3d69383e097d245bafd1d8377d7.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97615220181101On permutably complemented subalgebras of finite dimensional Lie algebras1521121510.22034/as.2018.1215ENLeilaGoudarziDepartment of mathematics, University of Ayatollah Alozma Boroujerdi, Boroujerd, IranJournal Article20180331Let $L$ 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.https://as.yazd.ac.ir/article_1215_addd86682e26e2e4e9874fe0d2069411.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97615220181101Spectra of some new extended corona2334121610.22034/as.2018.1216ENMalihehTajarrodDepartment of Mathematics, Kerman Branch, Islamic Azad University, Kerman, IranTaherehSistaniDepartment of Mathematics, Kerman Branch, Islamic Azad University, Kerman, IranJournal Article20180823For 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.https://as.yazd.ac.ir/article_1216_0a6cc5868240f0394988d16861c2cbc9.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97615220181101Finite groups admitting a connected cubic integral bi-Cayley graph3543121710.22034/as.2018.1217ENMajidArezoomandUniversity of Larestan0000-0002-4614-6350BijanTaeriDepartment of mathematical sciences
Isfahan University of Technology
Isfahan, Iran.Journal Article20180322A 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.https://as.yazd.ac.ir/article_1217_916b135f40cc53c43df5d1406cdac745.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97615220181101No-homomorphism conditions for hypergraphs4553126310.22034/as.2018.1263ENSamanehTahmasebiFaculty of Mathematical Sciences
Shahrood university of Technology, Shahrood, Shahrood, Iran.SadeghRahimi SharbafFaculty of Mathematical Sciences
Shahrood university of Technology, Shahrood, Shahrood, Iran.Journal Article20180509In 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.https://as.yazd.ac.ir/article_1263_5837ea3e49312c8317d9598976971934.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97615220181101Internal Topology on MI-groups5578133310.22034/as.2018.1333ENHosseinBagheriDepartment of Mathematics, Yazd University, Yazd, IranS. Mohammad SadeghModaresDepartment of Mathematics,
Yazd University, Yazd, Iran.Journal Article20180204An 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.https://as.yazd.ac.ir/article_1333_05170bc08b6a871d90f675cf870931aa.pdf