2020-02-21T22:50:31Z
http://ijmc.kashanu.ac.ir/?_action=export&rf=summon&issue=857
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
Autobiography of IVAN GUTMAN
I.
GUTMAN
2010
04
01
1
4
http://ijmc.kashanu.ac.ir/article_5128_025fbe1e83d02f1fe8cb43b602da986f.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
Wiener Way to Dimensionality
O.
ORI
F.
CATALDO
D.
VUKIČEVIĆ
A
GRAOVAC
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
2010
04
01
5
15
http://ijmc.kashanu.ac.ir/article_5150_6de0a526852fe0f62c2951d4172451bd.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
On Second Geometric-Arithmetic Index of Graphs
K.
DAS
I.
GUTMAN
B.
FURTULA
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
2010
04
01
17
28
http://ijmc.kashanu.ac.ir/article_5151_d31456f9d3923786c6852def2bdb8952.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
On Third Geometric-Arithmetic Index of Graphs
K.
DAS
I.
GUTMAN
B.
FURTULA
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
2010
04
01
29
36
http://ijmc.kashanu.ac.ir/article_5152_3f8b39102961616b12e394cdfc51c919.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
Some New Results On the Hosoya Polynomial of Graph Operations
H.
MOHAMADINEZHAD-RASHTI
H.
YOUSEFI-AZARI
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
2010
04
01
37
43
http://ijmc.kashanu.ac.ir/article_5153_4a3a57fbc78171abaef207326e14b456.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
Eccentric Connectivity Index: Extremal Graphs and Values
T.
DOŠLIĆ
M.
SAHELI
D.
VUKIČEVIĆ
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
2010
04
01
45
56
http://ijmc.kashanu.ac.ir/article_5154_3596a800067167a2d76a24fda346d9f6.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
Some Topological Indices of Nanostar Dendrimers
M.
GHORBANI
M.
SONGHORI
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
2010
04
01
57
65
http://ijmc.kashanu.ac.ir/article_5155_001f28821a3446f33adf6f54093b73d1.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
Some Lower Bounds for Estrada Index
B.
ZHOU
Z.
DU
Estrada index
Eigenvalues (of graph)
Spectral moments
Lower bounds
2010
04
01
67
72
http://ijmc.kashanu.ac.ir/article_5156_b5abf6a21ef9191afd2ed2ed0e250726.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
Topological Compression Factors of 2-Dimensional TUC4C8(R) Lattices and Tori
T.
DOŠLIĆ
A.
GRAOVAC
D.
VUKIČEVIĆ
F.
CATALDO
O.
ORI
A.
IRANMANESH
A.
ASHRAFI
F.
MOFTAKHAR
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
2010
04
01
73
80
http://ijmc.kashanu.ac.ir/article_5157_980a8f6666ab80bbd1230e6d506def34.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
A Fast Approach to the Detection of All-Purpose Hubs in Complex Networks with Chemical Applications
S.
RAJTMAJER
D.
VUKIČEVIĆ
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
2010
04
01
81
96
http://ijmc.kashanu.ac.ir/article_5158_e7348974c9083c796030f1b6bcb9a040.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
On General Sum-Connectivity Index of Benzenoid Systems and Phenylenes
SH.
CHEN
F.
XIA
J.
YANG
General sum-connectivity index
Benzenoid systems
Phenylene
Hexagonal squeeze
2010
04
01
97
104
http://ijmc.kashanu.ac.ir/article_5159_e8c14ffd3fcc72860fec6d79779a6925.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
Eccentric Connectivity and Augmented Eccentric Connectivity Indices of N-Branched Phenylacetylenes Nanostar Dendrimers
Z.
YARAHMADI
eccentric connectivity index
Augmented eccentric connectivity index
Nanostar
2010
04
01
105
110
http://ijmc.kashanu.ac.ir/article_5160_dc269a19d114002da7214c9b5a03f9fc.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
Some Topological Indices of Tetrameric 1,3-Adamantane
G.
FATH–TABAR
A.
AZAD
N.
ELAHINEZHAD
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
2010
04
01
111
118
http://ijmc.kashanu.ac.ir/article_5161_8e599d8a71d9221245ea807ae9e49da8.pdf