CONDITIONAL EXPECTATION IN THE KOPKA'S D-POSETS
Ramin
Kazemi
Imam Khomeini International University
author
text
article
2014
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
1
v.
2
no.
2014
77
84
http://as.yazd.ac.ir/article_493_4709f0a71f4179d0c6228380f2b592ea.pdf
INDEPENDENT SETS OF SOME GRAPHS ASSOCIATED TO COMMUTATIVE RINGS
Saeid
Alikhani
Yazd University
author
Saeed
Mirvakili
Payame Noor University
author
text
article
2014
eng
Let $G=(V,E)$ be a simple graph. A set $S\subseteq V$ 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 $R$.
Algebraic Structures and Their Applications
Yazd University
2382-9761
1
v.
2
no.
2014
85
103
http://as.yazd.ac.ir/article_494_9a959ffc1b7435033444f341ed9591ff.pdf
ON THE SZEGED INDEX OF NON-COMMUTATIVE GRAPH OF GENERAL LINEAR GROUP
Azizollah
Azad
Arak University
author
Nafiseh
Elahinezhad
Arak University
author
text
article
2014
eng
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 $G\setminus Z(G)$ as vertices of$\Gamma_G$ and joint two distinct vertices $x$ and $y$ whenever$yx\neq yx$. $\Gamma_G$ 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 $q\equiv 0 (mod~~4)$. In this paper we will compute the Szeged index for$\Gamma_{PSL(2,q)}$, where $q\not\equiv 0 (mod ~~ 4)$.
Algebraic Structures and Their Applications
Yazd University
2382-9761
1
v.
2
no.
2014
105
115
http://as.yazd.ac.ir/article_495_f25093403dee316a64647f1d8face225.pdf
A SHORT NOTE ON ATOMS AND COATOMS IN SUBGROUP LATTICES OF GROUPS
Hossain
Khass
University of Kashan
author
Behnam
Bazigaran
University of Kashan
author
Ali Reza
Ashrafi
University of Kashan
author
text
article
2015
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
1
v.
2
no.
2015
117
122
http://as.yazd.ac.ir/article_518_a4d945c8415d1f3e4cc6d623319445c0.pdf
NILPOTENT GRAPHS OF MATRIX ALGEBRAS
A.
Mahmoodi
Payame Noor University
author
text
article
2015
eng
Let $R$ be a ring with unity. The undirected nilpotent graph of $R$, denoted by $\Gamma_N(R)$, is a graph with vertex set ~$Z_N(R)^* = \{0\neq x \in R |\ xy \in N(R) \ for\ some\ y \in R^*\}$, 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 $n\geqslant 2$. 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 $\Gamma_{N}(M_{n}(R))\cong\Gamma_{N}(M_{n}(T(R)))$, where $T(R)$ be the total quotient ring of a commutative ring $R$
Algebraic Structures and Their Applications
Yazd University
2382-9761
1
v.
2
no.
2015
123
132
http://as.yazd.ac.ir/article_519_07a7feb6e66f4f6879ca8cc11e224da5.pdf
SIGNLESS LAPLACIAN SPECTRAL MOMENTS OF GRAPHS AND ORDERING SOME GRAPHS WITH RESPECT TO THEM
Fatemeh
Taghvaee
University of Kashan
author
Gholam Hossein
Fath-Tabar
University of Kashan
author
text
article
2014
eng
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 $T_k(G)=\sum_{i=1}^{n}q_i^{k}$, $k\geqslant 0$, 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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
1
v.
2
no.
2014
133
141
http://as.yazd.ac.ir/article_520_57b8555558526c827af33f7a15141f7f.pdf