2018-12-19T16:01:22Z
http://as.yazd.ac.ir/?_action=export&rf=summon&issue=111
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2014
1
1
THE ORDER GRAPHS OF GROUPS
SH.
Payrovi
H.
Pasebani
Let $G$ be a group. The order graph of $G$ is the (undirected)graph $Gamma(G)$,those whose vertices are non-trivial subgroups of $G$ and two distinctvertices $H$ and $K$ are adjacent if and only if either$o(H)|o(K)$ or $o(K)|o(H)$. In this paper, we investigate theinterplay between the group-theoretic properties of $G$ and thegraph-theoretic properties of $Gamma(G)$. For a finite group$G$, we show that $Gamma(G)$ is a connected graph with diameter at mosttwo, and $Gamma(G)$ is a complete graph ifand only if $G$ is a $p$-group for some prime number $p$. Furthermore,it is shown that $Gamma(G)=K_5$ if and only if either$Gcong C_{p^5}, C_3times C_3$, $C_2timesC_4$ or $Gcong Q_8$.
Finite group
Connected graph
star graph
2014
02
01
1
10
http://as.yazd.ac.ir/article_409_c5c1d4b6b27aef175b66fd0c85d2eac4.pdf
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2014
1
1
ENLARGED FUNDAMENTALLY VERY THIN Hv-STRUCTURES
T.
Vougiouklis
We study a new class of $H_v$-structures called Fundamentally Very Thin. This is an extension of the well known class of the Very Thin hyperstructures. We present applications of these hyperstructures.
Hyperstructures
$H_{v}$-structures
hopes
$partial$-hopes
2014
02
01
11
21
http://as.yazd.ac.ir/article_410_a84741ff38a501826228c29a144726fd.pdf
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2014
1
1
HYPERTRANSCENDENTAL FORMAL POWER SERIES OVER FIELDS OF POSITIVE CHARACTERISTIC
Habib
Sharif
Let $K$ be a field of characteristic$p>0$, $K[[x]]$, the ring of formal power series over $ K$,$K((x))$, the quotient field of $ K[[x]]$, and $ K(x)$ the fieldof rational functions over $K$. We shall give somecharacterizations of an algebraic function $fin K((x))$ over $K$.Let $L$ be a field of characteristic zero. The power series $finL[[x]]$ is called differentially algebraic, if it satisfies adifferential equation of the form $P(x, y, y',...)=0$, where $P$is a non-trivial polynomial. This notion is defined over fields ofcharacteristic zero and is not so significant over fields ofcharacteristic $p>0$, since $f^{(p)}=0$. We shall define ananalogue of the concept of a differentially algebraic power seriesover $K$ and we shall find some more related results.
Formal Power Series
Algebraic Formal Power Series
Differentially Algebraic Formal Power Series
2014
02
01
23
33
http://as.yazd.ac.ir/article_411_18804562d772712dfa86536f3e6ba671.pdf
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2014
1
1
STABILIZER TOPOLOGY OF HOOPS
R.A.
Borzooei
M.
Aaly Kologani
In this paper, we introduce the concepts of right, left and product stabilizers on hoops and study some properties and the relation between them. And we try to find that how they can be equal and investigate that under what condition they can be filter, implicative filter, fantastic and positive implicative filter. Also, we prove that right and product stabilizers are filters and if they are proper, then they are prime filters. Then by using the right stabilizers produce a basis for a topology on hoops. We show that the generated topology by this basis is Baire, connected, locally connected and separable and we investigate the other properties of this topology. Also, by the similar way, we introduce the right, left and product stabilizers on quotient hoops and introduce the quotient topology that is generated by them and investigate that under what condition this topology is Hausdorff space, $T_{0}$ or $T_{1}$ spaces.
Hoop algebra
stabilizer topology
Baire space
connected
locally connected
separable topology
2014
02
01
35
48
http://as.yazd.ac.ir/article_412_2b7660c436537a35bbc015e90365dd28.pdf
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2014
1
1
AUTOMORPHISM GROUP OF GROUPS OF ORDER pqr
M.
Ghorbani
F.
Nowroozi Larki
H"{o}lder in 1893 characterized all groups of order $pqr$ where $p>q>r$ are prime numbers. In this paper, by using new presentations of these groups, we compute their full automorphism group.
Affine group
Frobenius group
Automorphism group
2014
02
01
49
56
http://as.yazd.ac.ir/article_413_d618acbaf2f7c98f8667ef4ce3c65ab7.pdf
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2014
1
1
COSPECTRALITY MEASURES OF GRAPHS WITH AT MOST SIX VERTICES
A.
Abdollahi
Sh.
Janbaz
M.R.
Oboudi
Cospectrality of two graphs measures the differences between the ordered spectrum of these graphs in various ways. Actually, the origin of this concept came back to Richard Brualdi's problems that are proposed in cite{braldi}: Let $G_n$ and $G'_n$ be two nonisomorphic simple graphs on $n$ vertices with spectra$$lambda_1 geq lambda_2 geq cdots geq lambda_n ;;;text{and};;; lambda'_1 geq lambda'_2 geq cdots geq lambda'_n,$$ respectively. Define the distance between the spectra of $G_n$ and $G'_n$ as$$lambda(G_n,G'_n) =sum_{i=1}^n (lambda_i-lambda'_i)^2 ;;; big(text{or use}; sum_{i=1}^n|lambda_i-lambda'_i|big).$$Define the cospectrality of $G_n$ by$text{cs}(G_n) = min{lambda(G_n,G'_n) ;:; G'_n ;;text{not isomorphic to} ; G_n}.$Let $text{cs}_n = max{text{cs}(G_n) ;:; G_n ;;text{a graph on}; n ;text{vertices}}.$Investigation of $text{cs}(G_n)$ for special classes of graphs and finding a good upper bound on $text{cs}_n$ are two main questions in thissubject.In this paper, we briefly give some important results in this direction and then we collect all cospectrality measures of graphs with at most six vertices with respect to three norms. Also, we give the shape of all graphs that are closest (with respect to cospectrality measure) to a given graph $G$.
Spectra of graphs
edge deletion
adjacency matrix of a graph
2014
02
01
57
67
http://as.yazd.ac.ir/article_421_f8cdc6042860185defb4bc45c2b6542d.pdf