2011
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Hyperdiamonds: a Topological View
2
2
Hyperdiamonds are covalently bonded fullerenes in crystalline forms, more or less related to diamond, and having a significant amount of sp3 carbon atoms. Design of several hypothetical crystal networks was performed by using our original software programs CVNET and NANOSTUDIO. The topology of the networks is described in terms of the net parameters and several counting polynomials, calculated by NANOSTUDIO, OMEGA and PI software programs.
1

7
29


M.
DIUDEA
“BabesBolyai” University, Romania
“BabesBolyai” University, Romania
Romania


A.
ILIĆ
University of Niš,
Serbia
University of Niš,
Serbia
Serbia


M.
MEDELEANU
University “Politehnica”
Timisoara, Romania
University “Politehnica”
Timisoara,
Romania
Hyperdiamond
Crystallike network
Molecular topology
Counting polynomial
Evaluation of the Mineral Contents in Fish Meal by FT NIR using PLS and Kernel PLS
2
2
In the present work we study the use of Fourier transform near infrared spectroscopy (FTNIRS) technique to analysis the calcium (Ca), phosphorus (P) and copper (Cu) contents of fish meal. The regression methods employed were partial least squares (PLS) and kernel partial least squares (KPLS). The results showed that the efficiency of KPLS was better than PLS. As a whole, the application of FTNIRS with PLS and KPLS was as a suitable option for replacing the routine chemical analysis to assess the mineral content in fish meal, allowing immediate control of the fish meal without prior sample treatment or destruction.
1

31
38


S.
MASOUM
University of Kashan,
I. R. IRAN
University of Kashan,
I. R. IRAN
I R Iran


A.
ALISHAHI
Department of Fisheries and Environmental Science, Tehran University, Karaj, IRAN
Department of Fisheries and Environmental
I R Iran


M.
SHEKARCHI
Tehran University, IRAN
Tehran University, IRAN
I R Iran


H.
FARAHMAND
Sanitary Ministry of Iran, IRAN
Sanitary Ministry of Iran, IRAN
I R Iran
Calcium
Phosphorus
Copper
Fish meal
FTNIRS
KPLS
Eccentric and Total Eccentric Connectivity Indices of Caterpillars
2
2
Consider a simple connected graph with the vertex set . The eccentric and total connectivity indices of are defined as Σ and Σ , respectively. Here, denotes the degree of a vertex and is its eccentricity. In this paper, these two indices are calculated for a given arbitrary caterpillar.
1

39
44


KH.
FATHALIKHANI
University of Tehran, Tehran, Iran
University of Tehran, Tehran, Iran
I R Iran


H.
YOUSEFIAZARI
University of Tehran, Iran
University of Tehran, Iran
I R Iran
Eccentric connectivity index
Total eccentricity index
Caterpillar
Energy and Wiener Index of ZeroDivisor Graphs
2
2
Let R be a commutative ring and (R) be its zerodivisor graph. In this article, we study Wiener index and energy of Γ(Zn ) where n = pq or n = p2q and p, q are primes. A MATLAB code for our calculations is also presented.
1

45
51


M.
AHMADI
University
of Kashan, I. R. Iran
University
of Kashan, I. R. Iran
I R Iran


R.
JAHANINEZHAD
University
of Kashan, I. R. Iran
University
of Kashan, I. R. Iran
I R Iran
zerodivisor graph
Energy
Wiener index
The Clar Number of Fullerene C24n and Carbon Nanocone CNC4[n]
2
2
A fullerene graph is a 3−connected planar graph whose faces are pentagons and hexagons. The Clar number of a fullerene is the maximum size of sextet patterns, the sets of disjoint hexagons which are all Malternating for a Kekulé structure M of F. An exact formula of Clar number of some fullerene graphs and a class of carbon nanocones are obtained in this paper.
1

53
59


M.
GHORBANI
Shahid Rajaee Teacher Training
University, I. R. Iran
Shahid Rajaee Teacher Training
University,
I R Iran


E.
NASERPOUR
Shahid Rajaee Teacher Training
University, I. R. Iran
Shahid Rajaee Teacher Training
University,
I R Iran
Fullerene
Clar number
Sextet pattern
Carbon nanotube
Kekulé structure
The Eccentric Connectivity Index of Some Special Graphs
2
2
If is a connected graph with vertex set , then the eccentric connectivity index of , , is defined as Σ deg where deg is the degree of a vertex and is its eccentricity. Let A, B and C are families of graphs made by joining to , made by putting instead of each vertex in and made by putting instead of each vertex in , respectively. In this paper we compute the eccentric connectivity index of these families of graphs.
1

61
65


M.
IRANMANESH
Yazd University, Iran
Yazd University, Iran
I R Iran


R.
HAFEZIEH
Yazd University, Iran
Yazd University, Iran
I R Iran
Eccentric connectivity index
graph
Further Results on Wiener Polarity Index of Graphs
2
2
The Wiener polarity index Wp(G) of a molecular graph G of order n is the number of unordered pairs of vertices u, v of G such that the distance d(u,v) between u and v is 3. In an earlier paper, some extremal properties of this graph invariant in the class of catacondensed hexagonal systems and fullerene graphs were investigated. In this paper, some new bounds for this graph invariant are presented. A relationship between Wiener and Wiener polarity index of some classes of graphs are also presented.
1

67
70


A.
BEHMARAM
University of Tehran,
I. R. Iran
University of Tehran,
I. R. Iran
I R Iran


H.
YOUSEFIAZARI
Institute for Research in Fundamental Sciences (IPM), I. R. Iran
Institute for Research in Fundamental Sciences
I R Iran
Fullerene graph
Wiener index
Wiener polarity index
Hosoya Polynomial of an Infinite Family of Dendrimer Nanostar
2
2
Let G be a simple graph. The Hosoya polynomial of G is ( , ) , ( , ) = { , } ( ) xd u v H G x u v V G where d(u,v) denotes the distance between vertices u and v . The dendrimer nanostar is a part of a new group of macromolecules. In this paper we compute the Hosoya polynomial for an infinite family of dendrimer nanostar. As a consequence we obtain the Wiener index and the hyperWiener index of this dendrimer.
1

71
79


CH.
ESLAHCHI
Shahid Beheshti University, Iran
Shahid Beheshti University, Iran
I R Iran


S.
ALIKHANI
Yazd University, Iran
Yazd University, Iran
I R Iran


M.
AKHBARI
Islamic Azad University, Estahban Branch, Estahban, Iran
Islamic Azad University, Estahban Branch,
I R Iran
Hosoya polynomial
Wiener index
Dendrimer nanostar
diameter
On the Spectra of Reduced Distance Matrix of Thorn Graphs
2
2
Let G be a simple connected graph and {v1, v2, …, vk} be the set of pendent (vertices of degree one) vertices of G. The reduced distance matrix of G is a square matrix whose (i,j)– entry is the topological distance between vi and vj of G. In this paper, we obtain the spectrum of the reduced distance matrix of thorn graph of G, a graph which obtained by attaching some new vertices to pendent vertices of G. As an application we compute the spectrum of reduced distance matrix for some dendrimer graphs.
1

81
87


A.
HEYDARI
Arak Branch, Islamic Azad University, Arak, Iran
Arak Branch, Islamic Azad University, Arak,
I R Iran
Reduced distance matrix
Spectrum
Thorn graph
Dendrimer graphs
On the General Sum–Connectivity Co–Index of Graphs
2
2
In this paper, a new molecularstructure descriptor, the general sum–connectivity co–index is considered, which generalizes the first Zagreb co–index and the general sum– connectivity index of graph theory. We mainly explore the lower and upper bounds in terms of the order and size for this new invariant. Additionally, the Nordhaus–Gaddum–type result is also represented.
1

89
98


G.
SU
Beijing Institute of Technology, P. R. China
Beijing Institute of Technology, P. R. China
P. R. China


L.
XU
Changji University, P. R. China
Changji University, P. R. China
P. R. China
General sum–connectivity co–index
First Zagreb co–index
Lower and upper bounds
Distance Property of Fullerenes
2
2
Fullerenes are closed−cage carbon molecules formed by 12 pentagonal and n/2 – 10 hexagonal faces, where n is the number of carbon atoms. Patrick Fowler in his lecture in MCC 2009 asked about the Wiener index of fullerenes in general. In this paper we respond partially to this question for an infinite class of fullerenes with exactly 10n carbon atoms. Our method is general and can be applied to fullerene graphs with centrosymmetric adjacency matrix.
1

99
107


A.
GRAOVAC
University of Split, Croatia
University of Split, Croatia
Croatia


O.
ORI
Via Casilina Rome, Italy
Via Casilina Rome, Italy
Italy


M.
FAGHANI
University of Kashan, I. R. Iran
University of Kashan, I. R. Iran
I R Iran


A.
ASHRAFI
University of Kashan, I. R. Iran
University of Kashan, I. R. Iran
I R Iran
Fullerene
Wiener index
Centrosymmetric matrix
Computing Some Topological Indices of Tensor Product of Graphs
2
2
A topological index of a molecular graph G is a numeric quantity related to G which is invariant under symmetry properties of G. In this paper we obtain the Randić, geometricarithmetic, first and second Zagreb indices , first and second Zagreb coindices of tensor product of two graphs and then the Harary, Schultz and modified Schultz indices of tensor product of a graph G with complete graph of order n are obtained.
1

109
118


Z.
YARAHMADI
Khorramabad Branch, Islamic Azad University, I. R. Iran
Khorramabad Branch, Islamic Azad University,
I R Iran
Topological index
tensor product