2018-09-23T03:43:45Z
http://as.yazd.ac.ir/?_action=export&rf=summon&issue=121
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2014
1
2
CONDITIONAL EXPECTATION IN THE KOPKA'S D-POSETS
Ramin
Kazemi
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
2014
11
01
77
84
http://as.yazd.ac.ir/article_493_4709f0a71f4179d0c6228380f2b592ea.pdf
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2014
1
2
INDEPENDENT SETS OF SOME GRAPHS ASSOCIATED TO COMMUTATIVE RINGS
Saeid
Alikhani
Saeed
Mirvakili
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
2014
11
25
85
103
http://as.yazd.ac.ir/article_494_9a959ffc1b7435033444f341ed9591ff.pdf
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2014
1
2
ON THE SZEGED INDEX OF NON-COMMUTATIVE GRAPH OF GENERAL LINEAR GROUP
Azizollah
Azad
Nafiseh
Elahinezhad
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
2014
11
20
105
115
http://as.yazd.ac.ir/article_495_f25093403dee316a64647f1d8face225.pdf
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2014
1
2
A SHORT NOTE ON ATOMS AND COATOMS IN SUBGROUP LATTICES OF GROUPS
Hossain
Khass
Behnam
Bazigaran
Ali Reza
Ashrafi
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
2015
03
01
117
122
http://as.yazd.ac.ir/article_518_a4d945c8415d1f3e4cc6d623319445c0.pdf
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2014
1
2
NILPOTENT GRAPHS OF MATRIX ALGEBRAS
A.
Mahmoodi
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
2015
02
20
123
132
http://as.yazd.ac.ir/article_519_07a7feb6e66f4f6879ca8cc11e224da5.pdf
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2014
1
2
SIGNLESS LAPLACIAN SPECTRAL MOMENTS OF GRAPHS AND ORDERING SOME GRAPHS WITH RESPECT TO THEM
Fatemeh
Taghvaee
Gholam Hossein
Fath-Tabar
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
2014
12
31
133
141
http://as.yazd.ac.ir/article_520_57b8555558526c827af33f7a15141f7f.pdf