University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
2010
04
01
Autobiography of IVAN GUTMAN
1
4
EN
I.
GUTMAN
University of Kragujevac, Serbia
gutman@kg.ac.rs
10.22052/ijmc.2010.5128
http://ijmc.kashanu.ac.ir/article_5128.html
http://ijmc.kashanu.ac.ir/article_5128_025fbe1e83d02f1fe8cb43b602da986f.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
2010
04
01
Wiener Way to Dimensionality
5
15
EN
O.
ORI
Via Casilina, Italy
F.
CATALDO
Via Casilina, Italy
D.
VUKIČEVIĆ
University of Split, Croatia
A
GRAOVAC
The R. Bošković Institute”, Croatia
10.22052/ijmc.2010.5150
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=(s-2)-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.
Wiener dimensionality,Sierpinski fractals,Asymptotic Wiener index
http://ijmc.kashanu.ac.ir/article_5150.html
http://ijmc.kashanu.ac.ir/article_5150_6de0a526852fe0f62c2951d4172451bd.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
2010
04
01
On Second Geometric-Arithmetic Index of Graphs
17
28
EN
K.
CH.
DAS
Sungkyunkwan University, Republic of
Korea
I.
GUTMAN
University of Kragujevac, Serbia
B.
FURTULA
University of Kragujevac, Serbia
10.22052/ijmc.2010.5151
The concept of geometric-arithmetic 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 geometric-arithmetic index (GA2) and characterize the extremal graphs. Moreover, we establish Nordhaus-Gaddum-type results for GA2.
graph,Molecular Graph,First geometric-arithmetic index,Second
geometric-arithmetic index,Third geometric-arithmetic index
http://ijmc.kashanu.ac.ir/article_5151.html
http://ijmc.kashanu.ac.ir/article_5151_d31456f9d3923786c6852def2bdb8952.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
2010
04
01
On Third Geometric-Arithmetic Index of Graphs
29
36
EN
K.
CH.
DAS
Sungkyunkwan University, Republic of
Korea
I.
GUTMAN
University of Kragujevac, Serbia
B.
FURTULA
University of Kragujevac, Serbia
10.22052/ijmc.2010.5152
Continuing the work K. C. Das, I. Gutman, B. Furtula, On second geometric-arithmetic index of graphs, Iran. J. Math Chem., 1(2) (2010) 17-28, in this paper we present lower and upper bounds on the third geometric-arithmetic index GA3 and characterize the extremal graphs. Moreover, we give Nordhaus-Gaddum-type result for GA3.
graph,Molecular Graph,First geometric-arithmetic index,Second
geometric-arithmetic index,Third geometric-arithmetic index
http://ijmc.kashanu.ac.ir/article_5152.html
http://ijmc.kashanu.ac.ir/article_5152_3f8b39102961616b12e394cdfc51c919.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
2010
04
01
Some New Results On the Hosoya Polynomial of Graph Operations
37
43
EN
H.
MOHAMADINEZHAD-RASHTI
University of Tehran, Tehran,
I. R. Iran
H.
YOUSEFI-AZARI
University of Tehran, Tehran,
I. R. Iran
10.22052/ijmc.2010.5153
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 q-analog 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.
Wiener index,Wiener polynomial,Graph operation
http://ijmc.kashanu.ac.ir/article_5153.html
http://ijmc.kashanu.ac.ir/article_5153_4a3a57fbc78171abaef207326e14b456.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
2010
04
01
Eccentric Connectivity Index: Extremal Graphs and Values
45
56
EN
T.
DOŠLIĆ
University of Zagreb,
CROATIA
M.
SAHELI
University of Kashan,
I. R. IRAN
D.
VUKIČEVIĆ
University of Split , CROATIA
10.22052/ijmc.2010.5154
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.
eccentric connectivity index,Extremal graph
http://ijmc.kashanu.ac.ir/article_5154.html
http://ijmc.kashanu.ac.ir/article_5154_3596a800067167a2d76a24fda346d9f6.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
2010
04
01
Some Topological Indices of Nanostar Dendrimers
57
65
EN
M.
GHORBANI
Shahid Rajaee Teacher Training
University, I. R. Iran
M.
SONGHORI
Shahid Rajaee Teacher Training
University, I. R. Iran
10.22052/ijmc.2010.5155
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.
Wiener index,Szeged index,Randić index,Zagreb index,ABC Index,GA Index,Nanostar dendrimers
http://ijmc.kashanu.ac.ir/article_5155.html
http://ijmc.kashanu.ac.ir/article_5155_001f28821a3446f33adf6f54093b73d1.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
2010
04
01
Some Lower Bounds for Estrada Index
67
72
EN
B.
ZHOU
South China Normal University, China
Z.
DU
South China Normal University, China
10.22052/ijmc.2010.5156
Estrada index,Eigenvalues (of graph),Spectral moments,Lower bounds
http://ijmc.kashanu.ac.ir/article_5156.html
http://ijmc.kashanu.ac.ir/article_5156_b5abf6a21ef9191afd2ed2ed0e250726.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
2010
04
01
Topological Compression Factors of 2-Dimensional TUC4C8(R) Lattices and Tori
73
80
EN
T.
DOŠLIĆ
University of Zagreb,
Croatia
A.
GRAOVAC
The “Ruđer Bošković” Institute, Croatia
D.
VUKIČEVIĆ
University of Split, Croatia
F.
CATALDO
Actinium Chemical Research, Via Casilina , Italy
O.
ORI
Actinium Chemical Research, Via Casilina Italy
A.
IRANMANESH
Tarbiat Modaress University, Tehran, Iran
A.
R.
ASHRAFI
University of Kashan, Iran
F.
K.
MOFTAKHAR
University of Kashan, Iran
10.22052/ijmc.2010.5157
We derived explicit formulae for the eccentric connectivity index and Wiener index of 2-dimensional square-octagonal TUC4C8(R) lattices with open and closed ends. New compression factors for both indices are also computed in the limit N-->∞.
2-Dimensional square-octagonal lattice,eccentric connectivity index,Wiener index,Topological compression factors
http://ijmc.kashanu.ac.ir/article_5157.html
http://ijmc.kashanu.ac.ir/article_5157_980a8f6666ab80bbd1230e6d506def34.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
2010
04
01
A Fast Approach to the Detection of All-Purpose Hubs in Complex Networks with Chemical Applications
81
96
EN
S.
M.
RAJTMAJER
University of Dubrovnik, Croatia
D.
VUKIČEVIĆ
University of Split, Croatia
10.22052/ijmc.2010.5158
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 all-purpose network hubs. Several theoretical and real world chemical and biological networks are tested and results are analyzed.
Chemical networks,Complex networks,Network hubs,Vertex centrality
http://ijmc.kashanu.ac.ir/article_5158.html
http://ijmc.kashanu.ac.ir/article_5158_e7348974c9083c796030f1b6bcb9a040.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
2010
04
01
On General Sum-Connectivity Index of Benzenoid Systems and Phenylenes
97
104
EN
SH.
CHEN
Hunan City University, P. R. China
F.
XIA
Hunan City University, P. R. China
J.
YANG
Hunan City University, P. R. China
10.22052/ijmc.2010.5159
General sum-connectivity index,Benzenoid systems,Phenylene,Hexagonal squeeze
http://ijmc.kashanu.ac.ir/article_5159.html
http://ijmc.kashanu.ac.ir/article_5159_e8c14ffd3fcc72860fec6d79779a6925.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
2010
04
01
Eccentric Connectivity and Augmented Eccentric Connectivity Indices of N-Branched Phenylacetylenes Nanostar Dendrimers
105
110
EN
Z.
YARAHMADI
Islamic Azad University, Khorramabad Branch,
I. R. Iran
10.22052/ijmc.2010.5160
eccentric connectivity index,Augmented eccentric connectivity index,Nanostar
http://ijmc.kashanu.ac.ir/article_5160.html
http://ijmc.kashanu.ac.ir/article_5160_dc269a19d114002da7214c9b5a03f9fc.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
2010
04
01
Some Topological Indices of Tetrameric 1,3-Adamantane
111
118
EN
G.
H.
FATH–TABAR
University of Kashan, I R. Iran
A.
AZAD
Arak University,
I. R. Iran
N.
ELAHINEZHAD
Arak University,
I. R. Iran
10.22052/ijmc.2010.5161
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.
PI index,Szeged index,Zagreb index,Tetrameric 1,3–adamatane
http://ijmc.kashanu.ac.ir/article_5161.html
http://ijmc.kashanu.ac.ir/article_5161_8e599d8a71d9221245ea807ae9e49da8.pdf