eng
Yazd University
Algebraic Structures and Their Applications
2382-9761
2423-3447
2014-11-01
1
2
77
84
493
مقاله پژوهشی
CONDITIONAL EXPECTATION IN THE KOPKA'S D-POSETS
Ramin Kazemi
r.kazemi@sci.ikiu.ac.ir
1
Imam Khomeini International University
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.
http://as.yazd.ac.ir/article_493_4709f0a71f4179d0c6228380f2b592ea.pdf
Kopka's $D$-posets
random
variables
conditional expectation
eng
Yazd University
Algebraic Structures and Their Applications
2382-9761
2423-3447
2014-11-25
1
2
85
103
494
مقاله پژوهشی
INDEPENDENT SETS OF SOME GRAPHS ASSOCIATED TO COMMUTATIVE RINGS
Saeid Alikhani
alikhani@yazd.ac.ir
1
Saeed Mirvakili
saeed_mirvakili@yahoo.com
2
Yazd University
Payame Noor University
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 $R$.
http://as.yazd.ac.ir/article_494_9a959ffc1b7435033444f341ed9591ff.pdf
Independent set
Independence number
Zero-divisor graph, Ideal
eng
Yazd University
Algebraic Structures and Their Applications
2382-9761
2423-3447
2014-11-20
1
2
105
115
495
ON THE SZEGED INDEX OF NON-COMMUTATIVE GRAPH OF GENERAL LINEAR GROUP
Azizollah Azad
a-azad@araku.ac.ir
1
Nafiseh Elahinezhad
a.azad1347@gmail.com
2
Arak University
Arak University
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 $qnotequiv 0 (mod ~~ 4)$.
http://as.yazd.ac.ir/article_495_f25093403dee316a64647f1d8face225.pdf
Non-commuting grapg
general Linear group
Szeged index
eng
Yazd University
Algebraic Structures and Their Applications
2382-9761
2423-3447
2015-03-01
1
2
117
122
518
مقاله پژوهشی
A SHORT NOTE ON ATOMS AND COATOMS IN SUBGROUP LATTICES OF GROUPS
Hossain Khass
1
Behnam Bazigaran
2
Ali Reza Ashrafi
3
University of Kashan
University of Kashan
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.
http://as.yazd.ac.ir/article_518_a4d945c8415d1f3e4cc6d623319445c0.pdf
Atom
Coatom
group
Lattice
eng
Yazd University
Algebraic Structures and Their Applications
2382-9761
2423-3447
2015-02-20
1
2
123
132
519
مقاله پژوهشی
NILPOTENT GRAPHS OF MATRIX ALGEBRAS
A. Mahmoodi
1
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 $R$
http://as.yazd.ac.ir/article_519_07a7feb6e66f4f6879ca8cc11e224da5.pdf
zero-divisor graph
Nilpotent Graph
Commutative Ring
eng
Yazd University
Algebraic Structures and Their Applications
2382-9761
2423-3447
2014-12-31
1
2
133
141
520
مقاله پژوهشی
SIGNLESS LAPLACIAN SPECTRAL MOMENTS OF GRAPHS AND ORDERING SOME GRAPHS WITH RESPECT TO THEM
Fatemeh Taghvaee
1
Gholam Hossein Fath-Tabar
gh.fathtabar@gmail.com
2
University of Kashan
University of Kashan
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.
http://as.yazd.ac.ir/article_520_57b8555558526c827af33f7a15141f7f.pdf
Spectral moments sequence
signless Laplacian
generalized Petersen graph
T−order