Padmakar V Khadikar-Curriculum Vitae
M.
DIUDEA
Babes-Bolyai University, Cluj, Romania
author
A.
Manikpuri
Dept. of Chemistry, IPS Academy, Indore-452010, MP, India
author
S.
Karmarkar
Dept. of Chemistry, IPS Academy, Indore-452010, MP, India
author
text
article
2010
eng
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
no.
2010
1
6
https://ijmc.kashanu.ac.ir/article_5127_614a7ce8bd9a6e3ae333ee471d0696a3.pdf
dx.doi.org/10.22052/ijmc.2010.5127
Padmakar-Ivan Index in Nanotechnology
P.
KHADIKAR
Khatipura,
India
author
text
article
2010
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
no.
2010
7
42
https://ijmc.kashanu.ac.ir/article_5133_69608829fde8da3739d297fe668c4e85.pdf
dx.doi.org/10.22052/ijmc.2010.5133
Comparison of Topological Indices Based on Iterated ‘Sum’ versus ‘Product’ Operations
A.
BALABAN
Texas A&M University at Galveston, USA
author
P.
KHADIKAR
Khatipura, Indore
India
author
S.
AZIZ
Institute of Engineering and Technology, India
author
text
article
2010
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
no.
2010
43
67
https://ijmc.kashanu.ac.ir/article_5134_d70fc0d453920cc63e95881e6835da9e.pdf
dx.doi.org/10.22052/ijmc.2010.5134
Omega Polynomial in All R[8] Lattices
M.
DIUDEA
“Babes-Bolyai” University, Cluj,
Romania
author
text
article
2010
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
no.
2010
69
77
https://ijmc.kashanu.ac.ir/article_5135_463c4d3a0e2258ddb04ccb6462bc892c.pdf
dx.doi.org/10.22052/ijmc.2010.5135
Computation of the Sadhana (Sd) Index of Linear Phenylenes and Corresponding Hexagonal Sequences
S.
AZIZ
Institute of Engineering and Technology,
India
author
A.
MANIKPURI
IPS Academy, India
author
P.
JOHN
Technische Universitat Iimenau, Ilmenau
author
P.
KHADIKAR
Khatipura,
India
author
text
article
2010
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
no.
2010
79
90
https://ijmc.kashanu.ac.ir/article_5137_77cc2337e6077e5017bd6b709c9e11c1.pdf
dx.doi.org/10.22052/ijmc.2010.5137
Use of Structure Codes (Counts) for Computing Topological Indices of Carbon Nanotubes: Sadhana (Sd) Index of Phenylenes and its Hexagonal Squeezes
P.
JOHN
Technische Universitat Iimenau, Ilmenau
author
S.
AZIZ
Department of Applied Sciences (Mathematics), Indore
author
P.
KHADIKAR
Laxmi Fumigation and Pest Control, Khatipura, India.
author
text
article
2010
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
no.
2010
91
94
https://ijmc.kashanu.ac.ir/article_5138_27ded09e0fb14ea6a65bfd0082c84828.pdf
dx.doi.org/10.22052/ijmc.2010.5138
Second and Third Extremals of Catacondensed Hexagonal Systems with Respect to the PI Index
Z.
YARAHMADI
Islamic Azad University, Khorramabad Branch,
I. R. Iran
author
S.
MORADI
Arak University, Iran
author
text
article
2010
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
no.
2010
95
103
https://ijmc.kashanu.ac.ir/article_5139_1102d2fd97f933fa29079d6446627c4e.pdf
dx.doi.org/10.22052/ijmc.2010.5139
Computing Vertex PI, Omega and Sadhana Polynomials of F12(2n+1) Fullerenes
M.
GHORBANI
Shahid Rajaee Teacher Training
University, Iran
author
text
article
2010
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
no.
2010
105
110
https://ijmc.kashanu.ac.ir/article_5140_2a8c232a74e722a17ed57f7a0a5fc608.pdf
dx.doi.org/10.22052/ijmc.2010.5140
Sharp Bounds on the PI Spectral Radius
M.
NADJAFI-ARANI
University of Kashan, I. R. Iran
author
G.
FATH-TABAR
University of Kashan, I. R. Iran
author
M.
MIRZARGAR
University of Kashan, I. R. Iran
author
text
article
2010
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
no.
2010
111
117
https://ijmc.kashanu.ac.ir/article_5141_706f04cbcca81707a324490ab2279fde.pdf
dx.doi.org/10.22052/ijmc.2010.5141
Computation of Co-PI Index of TUC4C8(R) Nanotubes
F.
HASSANI
Payame Noor University, PNU Central Branch, Iran
author
O.
KHORMALI
Tarbiat Modares University, Iran
author
A.
IRANMANESH
Tarbiat Modares University,
Iran
author
text
article
2010
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
no.
2010
119
123
https://ijmc.kashanu.ac.ir/article_5142_619e84597c93a403ee5b4b0eaff4e4c0.pdf
dx.doi.org/10.22052/ijmc.2010.5142
Computing Vertex PI Index of Tetrathiafulvalene Dendrimers
H.
SHABANI
University of Kashan, I. R. Iran
author
text
article
2010
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
no.
2010
125
130
https://ijmc.kashanu.ac.ir/article_5143_7540ba516f7760926af890460197ac45.pdf
dx.doi.org/10.22052/ijmc.2010.5143
Computing PI and Hyper–Wiener Indices of Corona Product of some Graphs
M.
TAVAKOLI
University of Tehran,
Islamic Republic of Iran
author
H.
YOUSEFI–AZARI
University of Tehran,
Islamic Republic of Iran
author
text
article
2010
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
1
v.
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
no.
2010
131
135
https://ijmc.kashanu.ac.ir/article_5144_046652966c70f5ddcb1c002144947c5b.pdf
dx.doi.org/10.22052/ijmc.2010.5144