Autobiography of IVAN GUTMAN
I.
GUTMAN
University of Kragujevac, Serbia
author
text
article
2010
eng
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
no.
2010
1
4
http://ijmc.kashanu.ac.ir/article_5128_025fbe1e83d02f1fe8cb43b602da986f.pdf
dx.doi.org/10.22052/ijmc.2010.5128
Wiener Way to Dimensionality
O.
ORI
Via Casilina, Italy
author
F.
CATALDO
Via Casilina, Italy
author
D.
VUKIČEVIĆ
University of Split, Croatia
author
A
GRAOVAC
The R. Bošković Institute”, Croatia
author
text
article
2010
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
no.
2010
5
15
http://ijmc.kashanu.ac.ir/article_5150_6de0a526852fe0f62c2951d4172451bd.pdf
dx.doi.org/10.22052/ijmc.2010.5150
On Second Geometric-Arithmetic Index of Graphs
K.
DAS
Sungkyunkwan University, Republic of
Korea
author
I.
GUTMAN
University of Kragujevac, Serbia
author
B.
FURTULA
University of Kragujevac, Serbia
author
text
article
2010
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
no.
2010
17
28
http://ijmc.kashanu.ac.ir/article_5151_d31456f9d3923786c6852def2bdb8952.pdf
dx.doi.org/10.22052/ijmc.2010.5151
On Third Geometric-Arithmetic Index of Graphs
K.
DAS
Sungkyunkwan University, Republic of
Korea
author
I.
GUTMAN
University of Kragujevac, Serbia
author
B.
FURTULA
University of Kragujevac, Serbia
author
text
article
2010
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
no.
2010
29
36
http://ijmc.kashanu.ac.ir/article_5152_3f8b39102961616b12e394cdfc51c919.pdf
dx.doi.org/10.22052/ijmc.2010.5152
Some New Results On the Hosoya Polynomial of Graph Operations
H.
MOHAMADINEZHAD-RASHTI
University of Tehran, Tehran,
I. R. Iran
author
H.
YOUSEFI-AZARI
University of Tehran, Tehran,
I. R. Iran
author
text
article
2010
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
no.
2010
37
43
http://ijmc.kashanu.ac.ir/article_5153_4a3a57fbc78171abaef207326e14b456.pdf
dx.doi.org/10.22052/ijmc.2010.5153
Eccentric Connectivity Index: Extremal Graphs and Values
T.
DOŠLIĆ
University of Zagreb,
CROATIA
author
M.
SAHELI
University of Kashan,
I. R. IRAN
author
D.
VUKIČEVIĆ
University of Split , CROATIA
author
text
article
2010
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
no.
2010
45
56
http://ijmc.kashanu.ac.ir/article_5154_3596a800067167a2d76a24fda346d9f6.pdf
dx.doi.org/10.22052/ijmc.2010.5154
Some Topological Indices of Nanostar Dendrimers
M.
GHORBANI
Shahid Rajaee Teacher Training
University, I. R. Iran
author
M.
SONGHORI
Shahid Rajaee Teacher Training
University, I. R. Iran
author
text
article
2010
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
no.
2010
57
65
http://ijmc.kashanu.ac.ir/article_5155_001f28821a3446f33adf6f54093b73d1.pdf
dx.doi.org/10.22052/ijmc.2010.5155
Some Lower Bounds for Estrada Index
B.
ZHOU
South China Normal University, China
author
Z.
DU
South China Normal University, China
author
text
article
2010
eng
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
no.
2010
67
72
http://ijmc.kashanu.ac.ir/article_5156_b5abf6a21ef9191afd2ed2ed0e250726.pdf
dx.doi.org/10.22052/ijmc.2010.5156
Topological Compression Factors of 2-Dimensional TUC4C8(R) Lattices and Tori
T.
DOŠLIĆ
University of Zagreb,
Croatia
author
A.
GRAOVAC
The “Ruđer Bošković” Institute, Croatia
author
D.
VUKIČEVIĆ
University of Split, Croatia
author
F.
CATALDO
Actinium Chemical Research, Via Casilina , Italy
author
O.
ORI
Actinium Chemical Research, Via Casilina Italy
author
A.
IRANMANESH
Tarbiat Modaress University, Tehran, Iran
author
A.
ASHRAFI
University of Kashan, Iran
author
F.
MOFTAKHAR
University of Kashan, Iran
author
text
article
2010
eng
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-->∞.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
no.
2010
73
80
http://ijmc.kashanu.ac.ir/article_5157_980a8f6666ab80bbd1230e6d506def34.pdf
dx.doi.org/10.22052/ijmc.2010.5157
A Fast Approach to the Detection of All-Purpose Hubs in Complex Networks with Chemical Applications
S.
RAJTMAJER
University of Dubrovnik, Croatia
author
D.
VUKIČEVIĆ
University of Split, Croatia
author
text
article
2010
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
no.
2010
81
96
http://ijmc.kashanu.ac.ir/article_5158_e7348974c9083c796030f1b6bcb9a040.pdf
dx.doi.org/10.22052/ijmc.2010.5158
On General Sum-Connectivity Index of Benzenoid Systems and Phenylenes
SH.
CHEN
Hunan City University, P. R. China
author
F.
XIA
Hunan City University, P. R. China
author
J.
YANG
Hunan City University, P. R. China
author
text
article
2010
eng
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
no.
2010
97
104
http://ijmc.kashanu.ac.ir/article_5159_e8c14ffd3fcc72860fec6d79779a6925.pdf
dx.doi.org/10.22052/ijmc.2010.5159
Eccentric Connectivity and Augmented Eccentric Connectivity Indices of N-Branched Phenylacetylenes Nanostar Dendrimers
Z.
YARAHMADI
Islamic Azad University, Khorramabad Branch,
I. R. Iran
author
text
article
2010
eng
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
no.
2010
105
110
http://ijmc.kashanu.ac.ir/article_5160_dc269a19d114002da7214c9b5a03f9fc.pdf
dx.doi.org/10.22052/ijmc.2010.5160
Some Topological Indices of Tetrameric 1,3-Adamantane
G.
FATH–TABAR
University of Kashan, I R. Iran
author
A.
AZAD
Arak University,
I. R. Iran
author
N.
ELAHINEZHAD
Arak University,
I. R. Iran
author
text
article
2010
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
no.
2010
111
118
http://ijmc.kashanu.ac.ir/article_5161_8e599d8a71d9221245ea807ae9e49da8.pdf
dx.doi.org/10.22052/ijmc.2010.5161