eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
1
4
10.22052/ijmc.2010.5128
5128
Autobiography of IVAN GUTMAN
I. GUTMAN
gutman@kg.ac.rs
1
University of Kragujevac, Serbia
http://ijmc.kashanu.ac.ir/article_5128_025fbe1e83d02f1fe8cb43b602da986f.pdf
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
5
15
10.22052/ijmc.2010.5150
5150
Wiener Way to Dimensionality
O. ORI
1
F. CATALDO
2
D. VUKIČEVIĆ
3
A GRAOVAC
4
Via Casilina, Italy
Via Casilina, Italy
University of Split, Croatia
The R. Bošković Institute”, Croatia
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.
http://ijmc.kashanu.ac.ir/article_5150_6de0a526852fe0f62c2951d4172451bd.pdf
Wiener dimensionality
Sierpinski fractals
Asymptotic Wiener index
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
17
28
10.22052/ijmc.2010.5151
5151
On Second Geometric-Arithmetic Index of Graphs
K. DAS
1
I. GUTMAN
2
B. FURTULA
3
Sungkyunkwan University, Republic of Korea
University of Kragujevac, Serbia
University of Kragujevac, Serbia
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.
http://ijmc.kashanu.ac.ir/article_5151_d31456f9d3923786c6852def2bdb8952.pdf
Graph
Molecular graph
First geometric-arithmetic index
Second
geometric-arithmetic index
Third geometric-arithmetic index
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
29
36
10.22052/ijmc.2010.5152
5152
On Third Geometric-Arithmetic Index of Graphs
K. DAS
1
I. GUTMAN
2
B. FURTULA
3
Sungkyunkwan University, Republic of Korea
University of Kragujevac, Serbia
University of Kragujevac, Serbia
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.
http://ijmc.kashanu.ac.ir/article_5152_3f8b39102961616b12e394cdfc51c919.pdf
Graph
Molecular graph
First geometric-arithmetic index
Second
geometric-arithmetic index
Third geometric-arithmetic index
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
37
43
10.22052/ijmc.2010.5153
5153
Some New Results On the Hosoya Polynomial of Graph Operations
H. MOHAMADINEZHAD-RASHTI
1
H. YOUSEFI-AZARI
2
University of Tehran, Tehran, I. R. Iran
University of Tehran, Tehran, I. R. Iran
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.
http://ijmc.kashanu.ac.ir/article_5153_4a3a57fbc78171abaef207326e14b456.pdf
Wiener index
Wiener polynomial
Graph operation
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
45
56
10.22052/ijmc.2010.5154
5154
Eccentric Connectivity Index: Extremal Graphs and Values
T. DOŠLIĆ
1
M. SAHELI
2
D. VUKIČEVIĆ
3
University of Zagreb, CROATIA
University of Kashan, I. R. IRAN
University of Split , CROATIA
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.
http://ijmc.kashanu.ac.ir/article_5154_3596a800067167a2d76a24fda346d9f6.pdf
Eccentric connectivity index
Extremal graph
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
57
65
10.22052/ijmc.2010.5155
5155
Some Topological Indices of Nanostar Dendrimers
M. GHORBANI
1
M. SONGHORI
2
Shahid Rajaee Teacher Training University, I. R. Iran
Shahid Rajaee Teacher Training University, I. R. Iran
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.
http://ijmc.kashanu.ac.ir/article_5155_001f28821a3446f33adf6f54093b73d1.pdf
Wiener index
Szeged index
Randić index
Zagreb index
ABC Index
GA Index
Nanostar dendrimers
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
67
72
10.22052/ijmc.2010.5156
5156
Some Lower Bounds for Estrada Index
B. ZHOU
1
Z. DU
2
South China Normal University, China
South China Normal University, China
http://ijmc.kashanu.ac.ir/article_5156_b5abf6a21ef9191afd2ed2ed0e250726.pdf
Estrada index
Eigenvalues (of graph)
Spectral moments
Lower bounds
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
73
80
10.22052/ijmc.2010.5157
5157
Topological Compression Factors of 2-Dimensional TUC4C8(R) Lattices and Tori
T. DOŠLIĆ
1
A. GRAOVAC
2
D. VUKIČEVIĆ
3
F. CATALDO
4
O. ORI
5
A. IRANMANESH
6
A. ASHRAFI
7
F. MOFTAKHAR
8
University of Zagreb, Croatia
The “Ruđer Bošković” Institute, Croatia
University of Split, Croatia
Actinium Chemical Research, Via Casilina , Italy
Actinium Chemical Research, Via Casilina Italy
Tarbiat Modaress University, Tehran, Iran
University of Kashan, Iran
University of Kashan, Iran
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-->∞.
http://ijmc.kashanu.ac.ir/article_5157_980a8f6666ab80bbd1230e6d506def34.pdf
2-Dimensional square-octagonal lattice
Eccentric connectivity index
Wiener index
Topological compression factors
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
81
96
10.22052/ijmc.2010.5158
5158
A Fast Approach to the Detection of All-Purpose Hubs in Complex Networks with Chemical Applications
S. RAJTMAJER
1
D. VUKIČEVIĆ
2
University of Dubrovnik, Croatia
University of Split, Croatia
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.
http://ijmc.kashanu.ac.ir/article_5158_e7348974c9083c796030f1b6bcb9a040.pdf
Chemical networks
Complex networks
Network hubs
Vertex centrality
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
97
104
10.22052/ijmc.2010.5159
5159
On General Sum-Connectivity Index of Benzenoid Systems and Phenylenes
SH. CHEN
1
F. XIA
2
J. YANG
3
Hunan City University, P. R. China
Hunan City University, P. R. China
Hunan City University, P. R. China
http://ijmc.kashanu.ac.ir/article_5159_e8c14ffd3fcc72860fec6d79779a6925.pdf
General sum-connectivity index
Benzenoid systems
Phenylene
Hexagonal squeeze
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
105
110
10.22052/ijmc.2010.5160
5160
Eccentric Connectivity and Augmented Eccentric Connectivity Indices of N-Branched Phenylacetylenes Nanostar Dendrimers
Z. YARAHMADI
1
Islamic Azad University, Khorramabad Branch, I. R. Iran
http://ijmc.kashanu.ac.ir/article_5160_dc269a19d114002da7214c9b5a03f9fc.pdf
Eccentric connectivity index
Augmented eccentric connectivity index
Nanostar
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
111
118
10.22052/ijmc.2010.5161
5161
Some Topological Indices of Tetrameric 1,3-Adamantane
G. FATH–TABAR
1
A. AZAD
2
N. ELAHINEZHAD
3
University of Kashan, I R. Iran
Arak University, I. R. Iran
Arak University, I. R. Iran
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.
http://ijmc.kashanu.ac.ir/article_5161_8e599d8a71d9221245ea807ae9e49da8.pdf
PI index
Szeged index
Zagreb index
Tetrameric 1
3–adamatane