در هنگام جستجو کلمه در قسمت عنوان میتوانید کلمات مورد جستجو را با کاراکتر (-) جدا کنید.
کاربرد نوع شرط:
- جایگاه : پژوهشی
- مجله: Transactions on Combinatorics
- نوع مقاله: Journal Article
- کلمات کلیدی: Irregularity,degree deviation measure,chemical graph
- چکیده:
- چکیده انگلیسی: Let $G$ be an $n-$vertex graph with $m$ vertices. The degree deviation measure of $G$ is defined as $s(G)$ $=$ $sum_{vin V(G)}|deg_G(v)- frac{2m}{n}|,$ where $n$ and $m$ are the number of vertices and edges of $G$, respectively. The aim of this paper is to prove the Conjecture 4.2 of [J. A. de Oliveira, C. S. Oliveira, C. Justel and N. M. Maia de Abreu, Measures of irregularity of graphs, Pesq. Oper., 33 (2013) 383--398]. The degree deviation measure of chemical graphs under some conditions on the cyclomatic number is also computed.
- انتشار مقاله: 01-12-1398
- نویسندگان: Ali Ghalavand,Ali Reza Ashrafi
- مشاهده
- جایگاه : پژوهشی
- مجله: Transactions on Combinatorics
- نوع مقاله: Journal Article
- کلمات کلیدی: First Zagreb index,Second Zagreb index,Quasi Unicyclic graphs
- چکیده:
- چکیده انگلیسی: Let $G$ be a simple graph. The graph $G$ is called a quasi unicyclic graph if there exists a vertex $x in V(G)$ such that $G-x$ is a connected graph with a unique cycle. Moreover, the first and the second Zagreb indices of $G$ denoted by $M_1(G)$ and $M_2(G)$, are the sum of $deg^2(u)$ overall vertices $u$ in $G$ and the sum of $deg(u)deg(v)$ of all edges $uv$ of $G$, respectively. The first and the second Zagreb indices are defined relative to the degree of vertices. In this paper, sharp upper and lower bounds for the first and the second Zagreb indices of quasi unicyclic graphs are given.
- انتشار مقاله: 27-10-1397
- نویسندگان: Majid Aghel,Ahmad Erfanian,Ali Reza Ashrafi
- مشاهده
- جایگاه : پژوهشی
- مجله: Transactions on Combinatorics
- نوع مقاله: Journal Article
- کلمات کلیدی: First Zagreb index,Second Zagreb index,tetracyclic graph
- چکیده:
- چکیده انگلیسی: The first Zagreb index, $M_1(G)$, and second Zagreb index, $M_2(G)$, of the graph $G$ is defined as $M_{1}(G)=sum_{vin V(G)}d^{2}(v)$ and $M_{2}(G)=sum_{e=uvin E(G)}d(u)d(v),$ where $d(u)$ denotes the degree of vertex $u$. In this paper, the first and second maximum values of the first and second Zagreb indices
in the class of all $n-$vertex tetracyclic graphs are presented.- انتشار مقاله: 23-10-1394
- نویسندگان: Nader Habibi,Tayebeh Dehghan Zadeh,Ali Reza Ashrafi
- مشاهده
- جایگاه : پژوهشی
- مجله: Khayyam Journal of Mathematics
- نوع مقاله: Journal Article
- کلمات کلیدی: Commuting conjugacy class graph,Commuting graph,CA-group,quotient graph
- چکیده:
- چکیده انگلیسی: Let $G$ be a finite nonabelian group. The commuting conjugacy class graph $Gamma(G)$ is a simple graph with the noncentral conjugacy classes of $G$ as its vertex set and two distinct vertices $X$ and $Y$ in $Gamma(G)$ are adjacent if and only if there are $x in X$ and $y in Y$ with this property that $xy = yx$. The aim of this paper is to obtain the structure of the commuting conjugacy class graph of finite CA-groups. It is proved that this graph is a union of some complete graphs. The commuting conjugacy class graph of certain groups are also computed.
- انتشار مقاله: 26-11-1397
- نویسندگان: Mohammad Ali Salahshour,Ali Reza Ashrafi
- مشاهده
- جایگاه : پژوهشی
- مجله: Khayyam Journal of Mathematics
- نوع مقاله: Journal Article
- کلمات کلیدی: corona,Cayley graph,Hierarchical product,skew product,converse skew product,NEPS,strong product
- چکیده:
- چکیده انگلیسی: The aim of this paper is to investigate the behavior of Cayley graphs under some graph operations. It is proved that the NEPS, corona, hierarchical, strong, skew and converse skew products of Cayley graphs are again Cayley graphs under some conditions.
- انتشار مقاله: 17-09-1393
- نویسندگان: Nasrin Malekmohammadi,Ali Reza Ashrafi
- مشاهده
- جایگاه : پژوهشی
- مجله: International Journal of Group Theory
- نوع مقاله: Journal Article
- کلمات کلیدی: Cayley graph,normal edge-transitive,normal arc-transitive
- چکیده:
- چکیده انگلیسی: Darafsheh and Assari in [Normal edge-transitive Cayley graphs on non-abelian groups of order 4p, where p is a prime number, Sci. China Math., 56 (1) (2013) 213-219.] classified the connected normal edge transitive and 12−arc-transitive Cayley graph of groups of order 4p. In this paper we continue this work by classifying the connected Cayley graph of groups of order 2pq, p>q are primes. As a consequence it is proved that Cay(G,S) is a 12−arc-transitive Cayley graph of order 2pq, p>q if and only if |S| is an even integer greater than 2, S = T cup T^{-1} and T subseteq { cb^ja^{i} | 0 leq i leq p - 1}, 1 leq j leq q-1, such that T and T^{-1} are orbits of Aut(G,S) and
begin{eqnarray*} G &cong& langle a, b, c | a^p = b^q = c^2 = e, ac = ca, bc = cb, b^{-1}ab = a^r rangle, or\ G &cong& langle a, b, c | a^p = b^q = c^2 = e, c ac = a^{-1}, bc = cb, b^{-1}ab = a^r rangle, end{eqnarray*}
where r^q equiv 1 (mod p).- انتشار مقاله: 26-10-1392
- نویسندگان: Ali Reza Ashrafi,Bijan Soleimani
- مشاهده
- جایگاه : پژوهشی
- مجله: International Journal of Group Theory
- نوع مقاله: Journal Article
- کلمات کلیدی: Automorphism group,Power graph,generalized join
- چکیده:
- چکیده انگلیسی: Suppose $Gamma$ is a graph with $V(Gamma) = { 1, 2,dots, p}$ and $ mathcal{F} = {Gamma_1,dots, Gamma_p} $ is a family of graphs such that $n_j = |V(Gamma_j)|$, $1 leq j leq p$. Define $Lambda = Gamma[Gamma_1,dots, Gamma_p]$ to be a graph with vertex set $ V(Lambda)=bigcup_{j=1}^pV(Gamma_j)$ and edge set $E(Lambda)=big(bigcup_{j=1}^pE(Gamma_j)big)cupbig(bigcup_{ijin E(Gamma)}{uv;uin V(Gamma_i),vin V(Gamma_j)}big) $. The graph $ Lambda$ is called the $Gamma$-join of $ mathcal{F}$. The power graph $mathcal{P}(G)$ of a group $G$ is the graph which has the group elements as vertex set and two elements are adjacent if one is a power of the other. The aim of this paper is to prove that $mathcal{P}(mathbb{Z}_{n}) = K_{phi(n)+1} + Delta_n[K_{phi(d_1)}, K_{phi(d_2)},dots, K_{phi(d_{p})}]$, where $Delta_n$ is a graph with vertex and edge sets $V(Delta_n)={d_i | 1,nnot = d_i | n, 1leq ileq p}$ and $ E(Delta_n)={ d_id_j | d_i|d_j, 1leq i
Some results on the power graph of groups, The Extended Abstracts of the 44th Annual Iranian Mathematics Conference, 27-30 August 2013, Ferdowsi University of Mashhad, Iran]. Finally, we apply our results to obtain complete descriptions of the power graphs of some finite groups. - انتشار مقاله: 02-05-1393
- نویسندگان: Zeinab Mehranian,Ahmad Gholami,Ali Reza Ashrafi
- مشاهده
- جایگاه : پژوهشی
- مجله: Algebraic Structures and Their Applications
- نوع مقاله: Journal Article
- کلمات کلیدی: Automorphism group,$X-$join of graphs,reduced $X-$join of graphs
- چکیده:
- چکیده انگلیسی: Suppose $X$ is a simple graph. The $X-$join $Gamma$ of a set of
complete or empty graphs ${X_x }_{x in V(X)}$ is a simple graph with the following vertex and edge sets:
begin{eqnarray*}
V(Gamma) &=& {(x,y) | x in V(X) & y in
V(X_x) },\ E(Gamma) &=& {
(x,y)(x^prime,y^prime) | xx^prime in E(X) or else
x = x^prime & yy^prime in E(X_x)}.
end{eqnarray*}
The $X-$join graph $Gamma$ is said to be reduced if $x, y in V(X)$, $x ne y$ and $N_X(x) setminus { y} = N_X(y) setminus { x}$ imply that $(i)$ if $xy notin E(X)$ then the graphs $X_x$ or $X_y$ are non-empty; $(ii)$ if $xy in E(X)$ then $X_x$ or $X_y$ are not complete graphs. The aim of this paper is to explore how the graph theoretical properties of $X-$join of graphs effect on its automorphism group. Among other results we compute the automorphism group of reduced complete-empty $X-$join of graphs.- انتشار مقاله: 10-10-1396
- نویسندگان: Adel Tadayyonfar,Ali Reza Ashrafi
- مشاهده
- جایگاه : پژوهشی
- مجله: Algebraic Structures and Their Applications
- نوع مقاله: Journal Article
- کلمات کلیدی: Atom,Coatom,group,Lattice
- چکیده:
- چکیده انگلیسی: In this paper we give an elementary argument about the atoms and coatoms of the lattice
of all subgroups of a group. It is proved that an abelian group of finite exponent is strongly coatomic.- انتشار مقاله: 03-07-1393
- نویسندگان: Hossain Khass,Behnam Bazigaran,Ali Reza Ashrafi
- مشاهده