2010
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Autobiography of IVAN GUTMAN
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I.
GUTMAN
University of Kragujevac, Serbia
University of Kragujevac, Serbia
Serbia
gutman@kg.ac.rs
Wiener Way to Dimensionality
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This note introduces a new general conjecture correlating the dimensionality dT of an infinite lattice with N nodes to the asymptotic value of its Wiener Index W(N). In the limit of large N the general asymptotic behavior W(N)≈Ns is proposed, where the exponent s and dT are related by the conjectured formula s=2+1/dT allowing a new definition of dimensionality dW=(s2)1. Being related to the topological Wiener index, dW is therefore called Wiener dimensionality. Successful applications of this method to various infinite lattices (like graphene, nanocones, Sierpinski fractal triangle and carpet) testify the validity of the conjecture for infinite lattices.
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O.
ORI
Via Casilina, Italy
Via Casilina, Italy
Italy


F.
CATALDO
Via Casilina, Italy
Via Casilina, Italy
Italy


D.
VUKIČEVIĆ
University of Split, Croatia
University of Split, Croatia
Croatia


A
GRAOVAC
The R. Bošković Institute”, Croatia
The R. Bošković Institute”,
Croatia
Wiener dimensionality
Sierpinski fractals
Asymptotic Wiener index
On Second GeometricArithmetic Index of Graphs
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The concept of geometricarithmetic indices (GA) was put forward in chemical graph theory very recently. In spite of this, several works have already appeared dealing with these indices. In this paper we present lower and upper bounds on the second geometricarithmetic index (GA2) and characterize the extremal graphs. Moreover, we establish NordhausGaddumtype results for GA2.
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K.
DAS
Sungkyunkwan University, Republic of
Korea
Sungkyunkwan University, Republic of
Korea
South Korea


I.
GUTMAN
University of Kragujevac, Serbia
University of Kragujevac, Serbia
Serbia


B.
FURTULA
University of Kragujevac, Serbia
University of Kragujevac, Serbia
Serbia
graph
Molecular graph
First geometricarithmetic index
Second geometricarithmetic index
Third geometricarithmetic index
On Third GeometricArithmetic Index of Graphs
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Continuing the work K. C. Das, I. Gutman, B. Furtula, On second geometricarithmetic index of graphs, Iran. J. Math Chem., 1(2) (2010) 1728, in this paper we present lower and upper bounds on the third geometricarithmetic index GA3 and characterize the extremal graphs. Moreover, we give NordhausGaddumtype result for GA3.
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K.
DAS
Sungkyunkwan University, Republic of
Korea
Sungkyunkwan University, Republic of
Korea
South Korea


I.
GUTMAN
University of Kragujevac, Serbia
University of Kragujevac, Serbia
Serbia


B.
FURTULA
University of Kragujevac, Serbia
University of Kragujevac, Serbia
Serbia
graph
Molecular graph
First geometricarithmetic index
Second geometricarithmetic index
Third geometricarithmetic index
Some New Results On the Hosoya Polynomial of Graph Operations
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The Wiener index is a graph invariant that has found extensive application in chemistry. In addition to that a generating function, which was called the Wiener polynomial, who’s derivate is a qanalog of the Wiener index was defined. In an article, Sagan, Yeh and Zhang in [The Wiener Polynomial of a graph, Int. J. Quantun Chem., 60 (1996), 959969] attained what graph operations do to the Wiener polynomial. By considering all the results that Sagan et al. admitted for Wiener polynomial on graph operations for each two connected and nontrivial graphs, in this article we focus on deriving Wiener polynomial of graph operations, Join, Cartesian product, Composition, Disjunction and Symmetric difference on n graphs and Wiener indices of them.
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H.
MOHAMADINEZHADRASHTI
University of Tehran, Tehran,
I. R. Iran
University of Tehran, Tehran,
I. R. Iran
I R Iran


H.
YOUSEFIAZARI
University of Tehran, Tehran,
I. R. Iran
University of Tehran, Tehran,
I. R. Iran
I R Iran
Wiener index
Wiener polynomial
Graph operation
Eccentric Connectivity Index: Extremal Graphs and Values
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Eccentric connectivity index has been found to have a low degeneracy and hence a significant potential of predicting biological activity of certain classes of chemical compounds. We present here explicit formulas for eccentric connectivity index of various families of graphs. We also show that the eccentric connectivity index grows at most polynomially with the number of vertices and determine the leading coefficient in the asymptotic behavior.
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T.
DOŠLIĆ
University of Zagreb,
CROATIA
University of Zagreb,
CROATIA
Croatia


M.
SAHELI
University of Kashan,
I. R. IRAN
University of Kashan,
I. R. IRAN
I R Iran


D.
VUKIČEVIĆ
University of Split , CROATIA
University of Split , CROATIA
Croatia
Eccentric connectivity index
Extremal graph
Some Topological Indices of Nanostar Dendrimers
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Wiener index is a topological index based on distance between every pair of vertices in a graph G. It was introduced in 1947 by one of the pioneer of this area e.g, Harold Wiener. In the present paper, by using a new method introduced by klavžar we compute the Wiener and Szeged indices of some nanostar dendrimers.
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M.
GHORBANI
Shahid Rajaee Teacher Training
University, I. R. Iran
Shahid Rajaee Teacher Training
University,
I R Iran


M.
SONGHORI
Shahid Rajaee Teacher Training
University, I. R. Iran
Shahid Rajaee Teacher Training
University,
I R Iran
Wiener index
Szeged index
Randić index
Zagreb index
ABC Index
GA Index
Nanostar dendrimers
Some Lower Bounds for Estrada Index
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B.
ZHOU
South China Normal University, China
South China Normal University, China
P. R. China


Z.
DU
South China Normal University, China
South China Normal University, China
P. R. China
Estrada index
Eigenvalues (of graph)
Spectral moments
Lower bounds
Topological Compression Factors of 2Dimensional TUC4C8(R) Lattices and Tori
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We derived explicit formulae for the eccentric connectivity index and Wiener index of 2dimensional squareoctagonal TUC4C8(R) lattices with open and closed ends. New compression factors for both indices are also computed in the limit N>∞.
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T.
DOŠLIĆ
University of Zagreb,
Croatia
University of Zagreb,
Croatia
Croatia


A.
GRAOVAC
The “Ruđer Bošković” Institute, Croatia
The “Ruđer Bošković” Institute,
Croatia


D.
VUKIČEVIĆ
University of Split, Croatia
University of Split, Croatia
Croatia


F.
CATALDO
Actinium Chemical Research, Via Casilina , Italy
Actinium Chemical Research, Via Casilina
Italy


O.
ORI
Actinium Chemical Research, Via Casilina Italy
Actinium Chemical Research, Via Casilina
Italy


A.
IRANMANESH
Tarbiat Modaress University, Tehran, Iran
Tarbiat Modaress University, Tehran, Iran
I R Iran


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


F.
MOFTAKHAR
University of Kashan, Iran
University of Kashan, Iran
I R Iran
2Dimensional squareoctagonal lattice
Eccentric connectivity index
Wiener index
Topological compression factors
A Fast Approach to the Detection of AllPurpose Hubs in Complex Networks with Chemical Applications
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A novel algorithm for the fast detection of hubs in chemical networks is presented. The algorithm identifies a set of nodes in the network as most significant, aimed to be the most effective points of distribution for fast, widespread coverage throughout the system. We show that our hubs have in general greater closeness centrality and betweenness centrality than vertices with maximal degree, while having comparable or higher degree than vertices with greatest closeness centrality and betweenness centrality. As such, they serve as allpurpose network hubs. Several theoretical and real world chemical and biological networks are tested and results are analyzed.
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S.
RAJTMAJER
University of Dubrovnik, Croatia
University of Dubrovnik, Croatia
Croatia


D.
VUKIČEVIĆ
University of Split, Croatia
University of Split, Croatia
Croatia
Chemical networks
Complex networks
Network hubs
Vertex centrality
On General SumConnectivity Index of Benzenoid Systems and Phenylenes
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104


SH.
CHEN
Hunan City University, P. R. China
Hunan City University, P. R. China
P. R. China


F.
XIA
Hunan City University, P. R. China
Hunan City University, P. R. China
P. R. China


J.
YANG
Hunan City University, P. R. China
Hunan City University, P. R. China
P. R. China
General sumconnectivity index
Benzenoid systems
Phenylene
Hexagonal squeeze
Eccentric Connectivity and Augmented Eccentric Connectivity Indices of NBranched Phenylacetylenes Nanostar Dendrimers
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105
110


Z.
YARAHMADI
Islamic Azad University, Khorramabad Branch,
I. R. Iran
Islamic Azad University, Khorramabad Branch,
I R Iran
Eccentric connectivity index
Augmented eccentric connectivity index
Nanostar
Some Topological Indices of Tetrameric 1,3Adamantane
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Topological indices are numerical parameters of a graph which characterize its topology. In this paper the PI, Szeged and Zagreb group indices of the tetrameric 1,3–adamantane are computed.
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G.
FATH–TABAR
University of Kashan, I R. Iran
University of Kashan, I R. Iran
I R Iran


A.
AZAD
Arak University,
I. R. Iran
Arak University,
I. R. Iran
I R Iran


N.
ELAHINEZHAD
Arak University,
I. R. Iran
Arak University,
I. R. Iran
I R Iran
PI index
Szeged index
Zagreb index
Tetrameric 1
3–adamatane