University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
2010
04
01
Padmakar V Khadikar-Curriculum Vitae
1
6
EN
M.
V.
DIUDEA
Babes-Bolyai University, Cluj, Romania
diudea@gmail.com
A.
D.
Manikpuri
Dept. of Chemistry, IPS Academy, Indore-452010, MP, India
S.
Karmarkar
Dept. of Chemistry, IPS Academy, Indore-452010, MP, India
10.22052/ijmc.2010.5127
http://ijmc.kashanu.ac.ir/article_5127.html
http://ijmc.kashanu.ac.ir/article_5127_614a7ce8bd9a6e3ae333ee471d0696a3.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
2010
04
01
Padmakar-Ivan Index in Nanotechnology
7
42
EN
P.
V.
KHADIKAR
Khatipura,
India
10.22052/ijmc.2010.5133
In this survey article a brief account on the development of Padmakar-Ivan (PI) index in that applications of Padmakar-Ivan (PI) index in the fascinating field of nano-technology are discussed.
Padmakar−Ivan index,Topological index,Carbon Nanotubes,Nanotechnology
http://ijmc.kashanu.ac.ir/article_5133.html
http://ijmc.kashanu.ac.ir/article_5133_69608829fde8da3739d297fe668c4e85.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
2010
04
01
Comparison of Topological Indices Based on Iterated ‘Sum’ versus ‘Product’ Operations
43
67
EN
A.
T.
BALABAN
Texas A&M University at Galveston, USA
P.
V.
KHADIKAR
Khatipura, Indore
India
S.
AZIZ
Institute of Engineering and Technology, India
10.22052/ijmc.2010.5134
The Padmakar-Ivan (PI) index is a first-generation topological index (TI) based on sums over all edges between numbers of edges closer to one endpoint and numbers of edges closer to the other endpoint. Edges at equal distances from the two endpoints are ignored. An analogous definition is valid for the Wiener index W, with the difference that sums are replaced by products. A few other TIs are discussed, and comparisons are made between them. The best correlation is observed between indices G and PI; satisfactory correlations exist between W/n3 and PI/n2, where n denotes the number of vertices in the hydrogen-depleted graph.
Topological indices,PI index,Balaban index J,Wiener index W,F and G indices
http://ijmc.kashanu.ac.ir/article_5134.html
http://ijmc.kashanu.ac.ir/article_5134_d70fc0d453920cc63e95881e6835da9e.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
2010
04
01
Omega Polynomial in All R[8] Lattices
69
77
EN
M.
V.
DIUDEA
“Babes-Bolyai” University, Cluj,
Romania
10.22052/ijmc.2010.5135
Omega polynomial Ω(, ) is defined on opposite edge strips ops in a graph G = G(V,E). The first and second derivatives, in X = 1, of Omega polynomial provide the Cluj-Ilmenau CI index. Close formulas for calculating these topological descriptors in an infinite lattice consisting of all R[8] faces, related to the famous Dyck graph, is given.
Omega polynomial,Dyck graph,Lattice, Map operations
http://ijmc.kashanu.ac.ir/article_5135.html
http://ijmc.kashanu.ac.ir/article_5135_463c4d3a0e2258ddb04ccb6462bc892c.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
2010
04
01
Computation of the Sadhana (Sd) Index of Linear Phenylenes and Corresponding Hexagonal Sequences
79
90
EN
S.
AZIZ
Institute of Engineering and Technology,
India
A.
D.
MANIKPURI
IPS Academy, India
P.
E.
JOHN
Technische Universitat Iimenau, Ilmenau
P.
KHADIKAR
Khatipura,
India
10.22052/ijmc.2010.5137
The Sadhana index (Sd) is a newly introduced cyclic index. Efficient formulae for calculating the Sd (Sadhana) index of linear phenylenes are given and a simple relation is established between the Sd index of phenylenes and of the corresponding hexagonal sequences.
Sd index,PI index,Phenylenes,Hexagonal chain
http://ijmc.kashanu.ac.ir/article_5137.html
http://ijmc.kashanu.ac.ir/article_5137_77cc2337e6077e5017bd6b709c9e11c1.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
2010
04
01
Use of Structure Codes (Counts) for Computing Topological Indices of Carbon Nanotubes: Sadhana (Sd) Index of Phenylenes and its Hexagonal Squeezes
91
94
EN
P.
E.
JOHN
Technische Universitat Iimenau, Ilmenau
S.
AZIZ
Department of Applied Sciences (Mathematics), Indore
P.
V.
KHADIKAR
Laxmi Fumigation and Pest Control, Khatipura, India.
10.22052/ijmc.2010.5138
Structural codes vis-a-vis structural counts, like polynomials of a molecular graph, are important in computing graph-theoretical descriptors which are commonly known as topological indices. These indices are most important for characterizing carbon nanotubes (CNTs). In this paper we have computed Sadhana index (Sd) for phenylenes and their hexagonal squeezes using structural codes (counts). Sadhana index is a very simple W-Sz-PItype topological index obtained by summing the number of edges on both sides of the elementary cuts of benzenoid graphs. It has the similar discriminating power as that of the Weiner (W)-, Szeged (Sz)-, and PI-indices.
Sadhana index,Graph-theoretical descriptor,Structural codes,Structural counts phenylene,Hexagonal squeeze,Benzenoids
http://ijmc.kashanu.ac.ir/article_5138.html
http://ijmc.kashanu.ac.ir/article_5138_27ded09e0fb14ea6a65bfd0082c84828.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
2010
04
01
Second and Third Extremals of Catacondensed Hexagonal Systems with Respect to the PI Index
95
103
EN
Z.
YARAHMADI
Islamic Azad University, Khorramabad Branch,
I. R. Iran
S.
MORADI
Arak University, Iran
10.22052/ijmc.2010.5139
The Padmakar-Ivan (PI) index is a Wiener-Szeged-like topological index which reflects certain structural features of organic molecules. The PI index of a graph G is the sum of all edges uv of G of the number of edges which are not equidistant from the vertices u and v. In this paper we obtain the second and third extremals of catacondensed hexagonal systems with respect to the PI index.
Topological index,PI index,Catacondensed hexagonal system
http://ijmc.kashanu.ac.ir/article_5139.html
http://ijmc.kashanu.ac.ir/article_5139_1102d2fd97f933fa29079d6446627c4e.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
2010
04
01
Computing Vertex PI, Omega and Sadhana Polynomials of F12(2n+1) Fullerenes
105
110
EN
M.
GHORBANI
Shahid Rajaee Teacher Training
University, Iran
10.22052/ijmc.2010.5140
The topological index of a graph G is a numeric quantity related to G which is invariant under automorphisms of G. The vertex PI polynomial is defined as PIv (G) euv nu (e) nv (e). Then Omega polynomial (G,x) for counting qoc strips in G is defined as (G,x) = cm(G,c)xc with m(G,c) being the number of strips of length c. In this paper, a new infinite class of fullerenes is constructed. The vertex PI, omega and Sadhana polynomials of this class of fullerenes are computed for the first time.
Fullerene,Vertex PI polynomial,Omega polynomial,Sadhana polynomial
http://ijmc.kashanu.ac.ir/article_5140.html
http://ijmc.kashanu.ac.ir/article_5140_2a8c232a74e722a17ed57f7a0a5fc608.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
2010
04
01
Sharp Bounds on the PI Spectral Radius
111
117
EN
M.
J.
NADJAFI-ARANI
University of Kashan, I. R. Iran
G.
H.
FATH-TABAR
University of Kashan, I. R. Iran
M.
MIRZARGAR
University of Kashan, I. R. Iran
10.22052/ijmc.2010.5141
In this paper some upper and lower bounds for the greatest eigenvalues of the PI and vertex PI matrices of a graph G are obtained. Those graphs for which these bounds are best possible are characterized.
PI Matrix,PI Energy,PI Spectral Radius
http://ijmc.kashanu.ac.ir/article_5141.html
http://ijmc.kashanu.ac.ir/article_5141_706f04cbcca81707a324490ab2279fde.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
2010
04
01
Computation of Co-PI Index of TUC4C8(R) Nanotubes
119
123
EN
F.
HASSANI
Payame Noor University, PNU Central Branch, Iran
O.
KHORMALI
Tarbiat Modares University, Iran
A.
IRANMANESH
Tarbiat Modares University,
Iran
10.22052/ijmc.2010.5142
In this paper, at first we introduce a new index with the name Co-PI index and obtain some properties related this new index. Then we compute this new index for TUC4C8(R) nanotubes.
Vertex-PI index,Co-PI index,TUC4C8 (R )Nanotube
http://ijmc.kashanu.ac.ir/article_5142.html
http://ijmc.kashanu.ac.ir/article_5142_619e84597c93a403ee5b4b0eaff4e4c0.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
2010
04
01
Computing Vertex PI Index of Tetrathiafulvalene Dendrimers
125
130
EN
H.
SHABANI
University of Kashan, I. R. Iran
10.22052/ijmc.2010.5143
General formulas are obtained for the vertex Padmakar-Ivan index (PIv) of tetrathiafulvalene (TTF) dendrimer, whereby TTF units we are employed as branching centers. The PIv index is a Wiener-Szeged-like index developed very recently. This topological index is defined as the summation of all sums of nu(e) and nv(e), over all edges of connected graph G.
Dendrimer nanostar,PIv index
http://ijmc.kashanu.ac.ir/article_5143.html
http://ijmc.kashanu.ac.ir/article_5143_7540ba516f7760926af890460197ac45.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
2010
04
01
Computing PI and Hyper–Wiener Indices of Corona Product of some Graphs
131
135
EN
M.
TAVAKOLI
University of Tehran,
Islamic Republic of Iran
H.
YOUSEFI–AZARI
University of Tehran,
Islamic Republic of Iran
10.22052/ijmc.2010.5144
Let G and H be two graphs. The corona product G o H is obtained by taking one copy of G and |V(G)| copies of H; and by joining each vertex of the i-th copy of H to the i-th vertex of G, i = 1, 2, …, |V(G)|. In this paper, we compute PI and hyper–Wiener indices of the corona product of graphs.
Topological indices,PI index,Hyper−Wiener index,Wiener index
http://ijmc.kashanu.ac.ir/article_5144.html
http://ijmc.kashanu.ac.ir/article_5144_046652966c70f5ddcb1c002144947c5b.pdf