2014
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The First Geometric–Arithmetic Index of Some Nanostar Dendrimers
2
2
Dendrimers are highly branched organic macromolecules with successive layers or generations of branch units surrounding a central core [1,4]. These are key molecules in nanotechnology and can be put to good use. In this article, we compute the first geometricarithmetic index of two infinite classes of dendrimers.
1

1
6


A.
Madanshekaf
Semnan University
Semnan University
Iran
amadanshekaf@semnan.ac.ir


M.
Moradi
Semnan University
Semnan University
Iran
Nanostar dendrimer
The first geometricarithmetic index
The Laplacian Polynomial and Kirchhoff Index of the kth Semi Total Point Graphs
2
2
The kth semi total point graph of a graph G, , is a graph obtained from G by adding k vertices corresponding to each edge and connecting them to the endpoints of edge considered. In this paper, a formula for Laplacian polynomial of in terms of characteristic and Laplacian polynomials of G is computed, where is a connected regular graph.The Kirchhoff index of is also computed.
1

7
15


Z.
Mehranian
Department of Mathematics, University of Qom, Qom, Iran
Department of Mathematics, University of
Iran
mehranian.z@gmail.com
Resistance distance
Kirchhoff index
Laplacian specturam
Derived graph
Flow Polynomial of some Dendrimers
2
2
Suppose G is an nvertex and medge simple graph with edge set E(G). An integervalued function f: E(G) → Z is called a ﬂow. Tutte was introduced the ﬂow polynomial F(G, λ) as a polynomial in an indeterminate λ with integer coefficients by F(G,λ) In this paper the Flow polynomial of some dendrimers are computed.
1

17
20


H.
Sharifi
Islamic Azad University
Islamic Azad University
Iran
sharifi_h@iust.ac.ir


G. H.
FathTabar
University of Kashan
University of Kashan
Iran
gh.fathtabar@gmail.com
Flow polynomial
Dendrimer
Graph
The Neighbourhood Polynomial of some Nanostructures
2
2
The neighbourhood polynomial G , is generating function for the number of faces of each cardinality in the neighbourhood complex of a graph. In other word $N(G,x)=sum_{Uin N(G)} x^{U}$, where N(G) is neighbourhood complex of a graph, whose vertices are the vertices of the graph and faces are subsets of vertices that have a common neighbour. In this paper we compute this polynomial for some nanostructures.
1

21
25


S.
Alikhani
Yazd University
Yazd University
Iran
alikhani206@gmail.com


E.
Mahmoudi
Yazd University
Yazd University
Iran
emahmoudi@yazd.ac.ir
Neighbourhood Polynomial
Dendrimer nanostar
Perfect Matchings in EdgeTransitive Graphs
2
2
We find recursive formulae for the number of perfect matchings in a graph G by splitting G into subgraphs H and Q. We use these formulas to count perfect matching of P hypercube Qn. We also apply our formulas to prove that the number of perfect matching in an edgetransitive graph is , where denotes the number of perfect matchings in G, is the graph constructed from by deleting edges with an end vertex in {u,v}.
1

27
33


A.
Marandi
University of Tehran
University of Tehran
Iran


A.
Nejah
University of Tehran
University of Tehran
Iran


A.
Behmaram
University of Tabriz
University of Tabriz
Iran
behmarammath@gmail.com
perfect matching
Edgetransitive graph
The Center and Periphery of Composite Graphs
2
2
The center (periphery) of a graph is the set of vertices with minimum (maximum) eccentricity. In this paper, the structure of centers and peripheries of some classes of composite graphs are determined. The relations between eccentricity, radius and diameter of such composite graphs are also investigated. As an application we determine the center and periphery of some chemical graphs such as nanotorus and nanotubes covered by C4.
1

35
44


Z.
Yarahmadi
Islamic Azad University
Islamic Azad University
Iran
z.yarahmadi@gmail.com


S.
Moradi
Arak Unversity
Arak Unversity
Iran
sirousmoradi@gmail.com
Eccentricity
radius
diameter
Center
periphery
Relation Between Wiener, Szeged and Detour Indices
2
2
In theoretical chemistry, molecular structure descriptors are used to compute properties of chemical compounds. Among them Wiener, Szeged and detour indices play significant roles in anticipating chemical phenomena. In the present paper, we study these topological indices with respect to their difference number.
1

45
51


N.
Azimi
Srtt Univ.
Srtt Univ.
Iran
ghorbani30@gmail.com


M.
Roumena
Srtt Univ.
Srtt Univ.
Iran
modjtaba.ghorbani@gmail.com


M.
Ghorbani
Department of mathematics, Shahid Rajaee Teacher Training University
Department of mathematics, Shahid Rajaee
Iran
mghorbani@sru.ac.ir
Wiener index
Szeged index
Detour index