Yazd University Algebraic Structures and Their Applications 2382-9761 2423-3447 1 2 2014 11 01 CONDITIONAL EXPECTATION IN THE KOPKA'S D-POSETS 77 84 EN Ramin Kazemi Imam Khomeini International University r.kazemi@sci.ikiu.ac.ir The notion of a \$D\$-poset was introduced in a connection withquantum mechanical models. In this paper, we introduce theconditional expectation of  random variables on theK^{o}pka's \$D\$-Poset and prove the basic properties ofconditional expectation on this  structure. Kopka's \$D\$-posets,random variables,conditional expectation http://as.yazd.ac.ir/article_493.html http://as.yazd.ac.ir/article_493_4709f0a71f4179d0c6228380f2b592ea.pdf
Yazd University Algebraic Structures and Their Applications 2382-9761 2423-3447 1 2 2014 11 25 INDEPENDENT SETS OF SOME GRAPHS ASSOCIATED TO COMMUTATIVE RINGS 85 103 EN Saeid Alikhani Yazd University alikhani@yazd.ac.ir Saeed Mirvakili Payame Noor University saeed_mirvakili@yahoo.com Let \$G=(V,E)\$ be a simple graph. A set \$Ssubseteq V\$ isindependent set of \$G\$,  if no two vertices of \$S\$ are adjacent.The  independence number \$alpha(G)\$ is the size of a maximumindependent set in the graph. In this paper we study and characterize the independent sets ofthe zero-divisor graph \$Gamma(R)\$ and ideal-based zero-divisor graph \$Gamma_I(R)\$of a commutative ring \$R\$. Independent set,Independence number,Zero-divisor graph, Ideal http://as.yazd.ac.ir/article_494.html http://as.yazd.ac.ir/article_494_9a959ffc1b7435033444f341ed9591ff.pdf
Yazd University Algebraic Structures and Their Applications 2382-9761 2423-3447 1 2 2014 11 20 ON THE SZEGED INDEX OF NON-COMMUTATIVE GRAPH OF GENERAL LINEAR GROUP 105 115 EN Azizollah Azad Arak University a-azad@araku.ac.ir Nafiseh Elahinezhad Arak University a.azad1347@gmail.com 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 number, chromatic number, Szeged index and  Wiener index play important role in graph theory. In particular, the clique number of non-commuting graph of some the general linear groups has been determined. nt Recently, Wiener and Szeged indiceshave been computed for \$Gamma_{PSL(2,q)}\$, where \$qequiv 0 (mod~~4)\$. In this paper we will compute the Szeged index for\$Gamma_{PSL(2,q)}\$, where \$qnotequiv 0 (mod ~~ 4)\$. Non-commuting grapg,general Linear group,Szeged index http://as.yazd.ac.ir/article_495.html http://as.yazd.ac.ir/article_495_f25093403dee316a64647f1d8face225.pdf
Yazd University Algebraic Structures and Their Applications 2382-9761 2423-3447 1 2 2015 03 01 A SHORT NOTE ON ATOMS AND COATOMS IN SUBGROUP LATTICES OF GROUPS 117 122 EN Hossain Khass University of Kashan Behnam Bazigaran University of Kashan Ali Reza Ashrafi University of Kashan In this paper we give an elementary argument about the atoms and coatoms of the latticeof all subgroups of a group. It is proved that an abelian group of finite exponent is strongly coatomic. Atom,Coatom,group,Lattice http://as.yazd.ac.ir/article_518.html http://as.yazd.ac.ir/article_518_a4d945c8415d1f3e4cc6d623319445c0.pdf
Yazd University Algebraic Structures and Their Applications 2382-9761 2423-3447 1 2 2015 02 20 NILPOTENT GRAPHS OF MATRIX ALGEBRAS 123 132 EN A. Mahmoodi Payame Noor University Let \$R\$ be a ring with unity. The undirected nilpotent graph of \$R\$, denoted by \$Gamma_N(R)\$, is a graph with vertex set ~\$Z_N(R)^* = {0neq x in R | xy in N(R) for some y in R^*}\$, and two distinct vertices \$x\$ and \$y\$ are adjacent if and only if \$xy in N(R)\$, or equivalently, \$yx in N(R)\$, where \$N(R)\$ denoted the nilpotent elements of \$R\$. Recently, it has been proved that if \$R\$ is a left Artinian ring, then \$diam(Gamma_{N}(R))leqslant 3\$. In this paper, using the concept of rank over commutative rings, we investigate basic properties of undirected nilpotent graph of matrix algebras. Moreover, some result on undirected nilpotent graph of matrix algebras over commutative rings are given. For instance, we prove that \$Gamma_{N}(M_{n}(R))\$ is not planar for all \$ngeqslant 2\$. Furthermore, we show that \$diam(Gamma_{N}(R))leqslant diam(Gamma_{N}(M_{n}(R)))\$ for an Artinian commutative ring \$R\$. Also, we prove that \$Gamma_{N}(M_{n}(R))congGamma_{N}(M_{n}(T(R)))\$, where \$T(R)\$ be the total quotient ring of a commutative ring \$R\$ zero-divisor graph,Nilpotent Graph,Commutative Ring http://as.yazd.ac.ir/article_519.html http://as.yazd.ac.ir/article_519_07a7feb6e66f4f6879ca8cc11e224da5.pdf
Yazd University Algebraic Structures and Their Applications 2382-9761 2423-3447 1 2 2014 12 31 SIGNLESS LAPLACIAN SPECTRAL MOMENTS OF GRAPHS AND ORDERING SOME GRAPHS WITH RESPECT TO THEM 133 141 EN Fatemeh Taghvaee University of Kashan Gholam Hossein Fath-Tabar University of Kashan gh.fathtabar@gmail.com Let \$G = (V, E)\$ be a simple graph. Denote by \$D(G)\$ the diagonal matrix \$diag(d_1,cdots,d_n)\$, where \$d_i\$ is the degree of vertex \$i\$  and  \$A(G)\$ the adjacency matrix of \$G\$. The  signless Laplacianmatrix of \$G\$ is \$Q(G) = D(G) + A(G)\$ and the \$k-\$th signless Laplacian spectral moment of  graph \$G\$ is defined as \$T_k(G)=sum_{i=1}^{n}q_i^{k}\$, \$kgeqslant 0\$, where \$q_1\$,\$q_2\$, \$cdots\$, \$q_n\$ are the eigenvalues of the signless Laplacian matrix of \$G\$. In this paper we first compute  the \$k-\$th signless Laplacian  spectral moments of a graph for small \$k\$  and then we order some graphs with respect to the signless Laplacian  spectral moments. Spectral moments sequence,signless Laplacian,generalized Petersen graph,T−order http://as.yazd.ac.ir/article_520.html http://as.yazd.ac.ir/article_520_57b8555558526c827af33f7a15141f7f.pdf