2011
2
2
2
118
A Survey on Omega Polynomial of Some Nano Structures
2
2
1

1
65


M.
Ghorbani
Shahid Rajaee Teacher Training
University, I. R. Iran
Shahid Rajaee Teacher Training
University,
Iran
mghorbani@sru.ac.ir
Omega polynomial
Sadhana polynomial
Fullerene
Nanotube
Remarks on DistanceBalanced Graphs
2
2
Distancebalanced graphs are introduced as graphs in which every edge uv has the following property: the number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. Basic properties of these graphs are obtained. In this paper, we study the conditions under which some graph operations produce a distancebalanced graph.
1

67
71


M.
TAVAKOLI
University of Tehran,
I. R. Iran
University of Tehran,
I. R. Iran
Iran


H.
YOUSEFIAZARI
University of Tehran,
I. R. Iran
University of Tehran,
I. R. Iran
Iran
Distancebalanced graphs
Graph operation
Computing the First and Third Zagreb Polynomials of Cartesian Product of Graphs
2
2
Let G be a graph. The first Zagreb polynomial M1(G, x) and the third Zagreb polynomial M3(G, x) of the graph G are defined as: ( ) ( , ) [ ] e uv E G G x x d(u) + d(v) M1 , ( , ) euvE(G) G x xd(u)  d(v) M3 . In this paper, we compute the first and third Zagreb polynomials of Cartesian product of two graphs and a type of dendrimers.
1

73
78


A.
ASTANEHASL
Islamic Azad University, Arak Branch,
I. R. Iran
Islamic Azad University, Arak Branch,
I.
Iran


GH.
FATHTABAR
University of Kashan,
I. R. Iran
University of Kashan,
I. R. Iran
Iran
Zagreb polynomial
Zagreb index
Graph
Wiener Index of a New Type of Nanostar Dendrimer
2
2
Let G be a molecular graph. The Wiener index of G is defined as the summation of all distances between vertices of G. In this paper, an exact formula for the Wiener index of a new type of nanostar dendrimer is given.
1

79
85


Z.
SADRI IRANI
Islamic Azad University, Falavarjan
Branch, I. R. Iran
Islamic Azad University, Falavarjan
Branch,
Iran


A.
KARBASIOUN
Islamic Azad University, Falavarjan
Branch, I. R. Iran
Islamic Azad University, Falavarjan
Branch,
Iran
Nanostar dendrimer
Molecular Graph
Wiener index
PI, Szeged and Revised Szeged Indices of IPR Fullerenes
2
2
In this paper PI, Szeged and revised Szeged indices of an infinite family of IPR fullerenes with exactly 60+12n carbon atoms are computed. A GAP program is also presented that is useful for our calculations.
1

87
99


A.
MOTTAGHI
University of Kashan,
I. R. Iran
University of Kashan,
I. R. Iran
Iran


Z.
MEHRANIAN
University of Kashan,
I. R. Iran
University of Kashan,
I. R. Iran
Iran
IPR fullerene
Szeged index
Revised Szeged index
PI index
A Note on the First GeometricArithmetic Index of Hexagonal Systems and Phenylenes
2
2
The first geometricarithmetic index was introduced in the chemical theory as the summation of 2 du dv /(du dv ) overall edges of the graph, where du stand for the degree of the vertex u. In this paper we give the expressions for computing the first geometricarithmetic index of hexagonal systems and phenylenes and present new method for describing hexagonal system by corresponding a simple graph to each hexagonal system.
1

101
108


Z.
YARAHMADI
Khorramabad Branch, Islamic Azad University,
I. R. Iran
Khorramabad Branch, Islamic Azad University,
Iran
Geometricarithmetic index
Hexagonal system
Phenylenes
Two Types of Geometric–Arithmetic Index of V–phenylenic Nanotube
2
2
The concept of geometricarithmetic indices was introduced in the chemical graph theory. These indices are defined by the following general formula: ( ) 2 ( ) uv E G u v u v Q Q Q Q GA G , where Qu is some quantity that in a unique manner can be associated with the vertex u of graph G. In this paper the exact formula for two types of geometricarithmetic index of Vphenylenic nanotube are given.
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109
117


S.
MORADI
Arak University,
I. R. Iran
Arak University,
I. R. Iran
Iran


S.
BABARAHIM
Arak University,
I. R. Iran
Arak University,
I. R. Iran
Iran


M.
GHORBANI
Shahid Rajaee Teacher Training
University, I. R. Iran
Shahid Rajaee Teacher Training
University,
Iran
GA Index
V–phenylenic nanotube