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( Ali Reza Ashrafi ),( Modjtaba Ghorbani ) 대한금속재료학회(구 대한금속학회) 2010 재료마당 Vol.23 No.3
The modified eccentric connectivity polynomial of a molecular graph, G, is defined as A(G,x)=Σa∈V(G)nG(a)xεG(a) where εG(a) is the eccentricity of vertex a and nG(a) is the sum of the degrees of its neighborhoods. In this paper, the polynomial for three infinite classes of fullerenes is computed.
COUNTING THE CINTRALIZERS OF SOME FINITE GROUPS
Ashrafi, Ali Reza 한국전산응용수학회 2000 Journal of applied mathematics & informatics Vol.7 No.1
For a finite group G, #Cent(G) denotes the number of cen-tralizers of its clements. A group G is called n-centralizer if #Cent( G) = n. and primitive n-centralizer if #Cent(G) = #Cent(${\frac}{G}{Z(G)$) = n. In this paper we compute the number of distinct centralizers of some finite groups and investigate the structure of finite groups with Qxactly SLX distinct centralizers. We prove that if G is a 6-centralizer group then ${\frac}{G}{Z(G)$${\cong}D_8$,$A_4$, $Z_2{\times}Z_2{\times}Z_2$ or $Z_2{\times}Z_2{\times}Z_2{\times}Z_2$.
On Diameter, Cyclomatic Number and Inverse Degree of Chemical Graphs
Reza Sharafdini,Ali Ghalavand,Ali Reza Ashrafi 경북대학교 자연과학대학 수학과 2020 Kyungpook mathematical journal Vol.60 No.3
Let G be a chemical graph with vertex set {v1, v1, . . . , vn} and degree sequence d(G) = (degG(v1), degG(v2), . . . , degG(vn)). The inverse degree, R(G) of G is defined as R(G) = Pni=11degG(vi). The cyclomatic number of G is defined as γ = m − n + k, where m, n and k are the number of edges, vertices and components of G, respectively. In this paper, some upper bounds on the diameter of a chemical graph in terms of its inverse degree are given. We also obtain an ordering of connected chemical graphs with respect to the inverse degree.
Calculation of Some Topological Indices of Splices and Links of Graphs
Ali Reza Ashrafi,Asma Hamzeh,Samaneh Hossein-Zadeh 한국전산응용수학회 2011 Journal of applied mathematics & informatics Vol.29 No.1
Explicit formulas are given for the first and second Zagreb index, degree-distance and Wiener-type invariants of splice and link of graphs. As a consequence, the first and second Zagreb coindex of these classes of composite graphs are also computed.
Ashrafi, Ali-Reza,Hamadanian, Masood 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.14 No.1
The non-rigid molecule group theory (NRG) in which the dynamical symmetry operations are defined as physical operations is a new field of chemistry. Smeyers in a series of papers applied this notion to determine the character table of restricted NRG of some molecules. In this work, a simple method is described, by means of which it is possible to calculate character tables for the symmetry group of molecules consisting of a number of NH3 groups attached to a rigid framework. We study the full non-rigid group (f-NRG) of tetraammineplatinum(II) with two separate symmetry groups C2v and C4v. We prove that they are groups of order 216 and 5184 with 27 and 45 conjugacy classes, respectively. Also, we will compute the character tables of these groups.
EXTREMAL CHEMICAL TREES WITH RESPECT TO HYPER-ZAGREB INDEX
Ali Ghalavand,Ali Reza Ashrafi,Reza Sharafdini,Ottorino Ori 한국수학교육학회 2019 純粹 및 應用數學 Vol.26 No.3
Suppose G is a molecular graph with edge set E(G). The Hyper-Zagreb index of G is defined as $ HM(G)=sum_{uv\in E(G)}[deg_{G}(u) + deg_{G}(v)]^2$, where $deg_G(u)$ is the degree of a vertex u in G. In this paper, we characterize the chemical trees of order $n=> 12$ with the first twenty smallest Hyper-Zagreb index are characterized.
ON FINITE GROUPS WITH A CERTAIN NUMBER OF CENTRALIZERS
REZA ASHRAFI, ALI,TAERI, BIJAN 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.17 No.1
Let G be a finite group and $\#$Cent(G) denote the number of centralizers of its elements. G is called n-centralizer if $\#$Cent(G) = n, and primitive n-centralizer if $\#$Cent(G) = $\#$Cent($\frac{G}{Z(G)}$) = n. In this paper we investigate the structure of finite groups with at most 21 element centralizers. We prove that such a group is solvable and if G is a finite group such that G/Z(G)$\simeq$$A_5$, then $\#$Cent(G) = 22 or 32. Moreover, we prove that As is the only finite simple group with 22 centralizers. Therefore we obtain a characterization of As in terms of the number of centralizers
ON FINITE GROUPS WITH EXACTLY SEVEN ELEMENT CENTRALIZERS
Ashrafi, Ali-Reza,Taeri, Bi-Jan 한국전산응용수학회 2006 Journal of applied mathematics & informatics Vol.22 No.1
For a finite group G, #Cent(G) denotes the number of centralizers of its elements. A group G is called n-centralizer if #Cent(G) = n, and primitive n-centralizer if #Cent(G) = #Cent($\frac{G}{Z(G)}$) = n. The first author in [1], characterized the primitive 6-centralizer finite groups. In this paper we continue this problem and characterize the primitive 7-centralizer finite groups. We prove that a finite group G is primitive 7-centralizer if and only if $\frac{G}{Z(G)}{\simeq}D_{10}$ or R, where R is the semidirect product of a cyclic group of order 5 by a cyclic group of order 4 acting faithfully. Also, we compute #Cent(G) for some finite groups, using the structure of G modulu its center.
GENERATING PAIRS FOR THE HELD GROUP He
Ashrafi, Ali-Reza 한국전산응용수학회 2002 Journal of applied mathematics & informatics Vol.10 No.1
A group G is said to be (l, n, n)-generated if it is a quotient group of the triangle group T(p,q,r)=(x,y,z|x$\^$p/=y$\^$q/=z$\^$r/=xyz=1). In [15], the question of finding all triples (l, m, n) such that non-abelian finite simple groups are (l , m, n)-generated was posed. In this paper we partially answer this question for the sporadic group He. We continue the study of (p, q, r) -generations of the sporadic simple groups, where p, q, r are distinct primes. The problem is resolved for the Held group He.
Group theory for tetraammineplatinum(II) with C_{2v} and C_{4v} point group in the non-rigid system
Ali Reza Ashrafi,Masood Hamadanian 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.14 No.-
The non-rigid molecule group theory (NRG) in which the dynamical symmetry operations are defined as physical operations is a new field of chemistry. Smeyers in a series of papers applied this notion to determine the character table of restricted NRG of some molecules. In this work, a simple method is described, by means of which it is possible to calculate character tables for the symmetry group of molecules consisting of a number of NH3 groups attached to a rigid framework. We study the full non-rigid group (f-NRG) of tetraammineplatinum(II) with two separate symmetry groups C2v and C4v. We prove that they are groups of order 216 and 5184 with 27 and 45 conjugacy classes, respectively. Also, we will compute the character tables of these groups.