ORIGINAL_ARTICLE
Padmakar V Khadikar-Curriculum Vitae
http://ijmc.kashanu.ac.ir/article_5127_614a7ce8bd9a6e3ae333ee471d0696a3.pdf
2010-04-01T11:23:20
2020-02-22T11:23:20
1
6
10.22052/ijmc.2010.5127
M.
DIUDEA
diudea@gmail.com
true
1
Babes-Bolyai University, Cluj, Romania
Babes-Bolyai University, Cluj, Romania
Babes-Bolyai University, Cluj, Romania
LEAD_AUTHOR
A.
Manikpuri
true
2
Dept. of Chemistry, IPS Academy, Indore-452010, MP, India
Dept. of Chemistry, IPS Academy, Indore-452010, MP, India
Dept. of Chemistry, IPS Academy, Indore-452010, MP, India
AUTHOR
S.
Karmarkar
true
3
Dept. of Chemistry, IPS Academy, Indore-452010, MP, India
Dept. of Chemistry, IPS Academy, Indore-452010, MP, India
Dept. of Chemistry, IPS Academy, Indore-452010, MP, India
AUTHOR
ORIGINAL_ARTICLE
Padmakar-Ivan Index in Nanotechnology
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.
http://ijmc.kashanu.ac.ir/article_5133_69608829fde8da3739d297fe668c4e85.pdf
2010-04-01T11:23:20
2020-02-22T11:23:20
7
42
10.22052/ijmc.2010.5133
Padmakar−Ivan index
topological index
Carbon nanotubes
Nanotechnology
P.
KHADIKAR
true
1
Khatipura,
India
Khatipura,
India
Khatipura,
India
AUTHOR
ORIGINAL_ARTICLE
Comparison of Topological Indices Based on Iterated ‘Sum’ versus ‘Product’ Operations
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.
http://ijmc.kashanu.ac.ir/article_5134_d70fc0d453920cc63e95881e6835da9e.pdf
2010-04-01T11:23:20
2020-02-22T11:23:20
43
67
10.22052/ijmc.2010.5134
Topological indices
PI index
Balaban index J
Wiener index W
F and G indices
A.
BALABAN
true
1
Texas A&M University at Galveston, USA
Texas A&M University at Galveston, USA
Texas A&M University at Galveston, USA
AUTHOR
P.
KHADIKAR
true
2
Khatipura, Indore
India
Khatipura, Indore
India
Khatipura, Indore
India
AUTHOR
S.
AZIZ
true
3
Institute of Engineering and Technology, India
Institute of Engineering and Technology, India
Institute of Engineering and Technology, India
AUTHOR
ORIGINAL_ARTICLE
Omega Polynomial in All R[8] Lattices
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.
http://ijmc.kashanu.ac.ir/article_5135_463c4d3a0e2258ddb04ccb6462bc892c.pdf
2010-04-01T11:23:20
2020-02-22T11:23:20
69
77
10.22052/ijmc.2010.5135
Omega polynomial
Dyck graph
Lattice, Map operations
M.
DIUDEA
true
1
“Babes-Bolyai” University, Cluj,
Romania
“Babes-Bolyai” University, Cluj,
Romania
“Babes-Bolyai” University, Cluj,
Romania
AUTHOR
ORIGINAL_ARTICLE
Computation of the Sadhana (Sd) Index of Linear Phenylenes and Corresponding Hexagonal Sequences
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.
http://ijmc.kashanu.ac.ir/article_5137_77cc2337e6077e5017bd6b709c9e11c1.pdf
2010-04-01T11:23:20
2020-02-22T11:23:20
79
90
10.22052/ijmc.2010.5137
Sd index
PI index
Phenylenes
Hexagonal chain
S.
AZIZ
true
1
Institute of Engineering and Technology,
India
Institute of Engineering and Technology,
India
Institute of Engineering and Technology,
India
AUTHOR
A.
MANIKPURI
true
2
IPS Academy, India
IPS Academy, India
IPS Academy, India
AUTHOR
P.
JOHN
true
3
Technische Universitat Iimenau, Ilmenau
Technische Universitat Iimenau, Ilmenau
Technische Universitat Iimenau, Ilmenau
AUTHOR
P.
KHADIKAR
true
4
Khatipura,
India
Khatipura,
India
Khatipura,
India
LEAD_AUTHOR
ORIGINAL_ARTICLE
Use of Structure Codes (Counts) for Computing Topological Indices of Carbon Nanotubes: Sadhana (Sd) Index of Phenylenes and its Hexagonal Squeezes
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.
http://ijmc.kashanu.ac.ir/article_5138_27ded09e0fb14ea6a65bfd0082c84828.pdf
2010-04-01T11:23:20
2020-02-22T11:23:20
91
94
10.22052/ijmc.2010.5138
Sadhana index
Graph-theoretical descriptor
Structural codes
Structural counts phenylene
Hexagonal squeeze
Benzenoids
P.
JOHN
true
1
Technische Universitat Iimenau, Ilmenau
Technische Universitat Iimenau, Ilmenau
Technische Universitat Iimenau, Ilmenau
AUTHOR
S.
AZIZ
true
2
Department of Applied Sciences (Mathematics), Indore
Department of Applied Sciences (Mathematics), Indore
Department of Applied Sciences (Mathematics), Indore
AUTHOR
P.
KHADIKAR
true
3
Laxmi Fumigation and Pest Control, Khatipura, India.
Laxmi Fumigation and Pest Control, Khatipura, India.
Laxmi Fumigation and Pest Control, Khatipura, India.
AUTHOR
ORIGINAL_ARTICLE
Second and Third Extremals of Catacondensed Hexagonal Systems with Respect to the PI Index
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.
http://ijmc.kashanu.ac.ir/article_5139_1102d2fd97f933fa29079d6446627c4e.pdf
2010-04-01T11:23:20
2020-02-22T11:23:20
95
103
10.22052/ijmc.2010.5139
topological index
PI index
Catacondensed hexagonal system
Z.
YARAHMADI
true
1
Islamic Azad University, Khorramabad Branch,
I. R. Iran
Islamic Azad University, Khorramabad Branch,
I. R. Iran
Islamic Azad University, Khorramabad Branch,
I. R. Iran
AUTHOR
S.
MORADI
true
2
Arak University, Iran
Arak University, Iran
Arak University, Iran
AUTHOR
ORIGINAL_ARTICLE
Computing Vertex PI, Omega and Sadhana Polynomials of F12(2n+1) Fullerenes
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.
http://ijmc.kashanu.ac.ir/article_5140_2a8c232a74e722a17ed57f7a0a5fc608.pdf
2010-04-01T11:23:20
2020-02-22T11:23:20
105
110
10.22052/ijmc.2010.5140
Fullerene
Vertex PI polynomial
Omega polynomial
Sadhana polynomial
M.
GHORBANI
true
1
Shahid Rajaee Teacher Training
University, Iran
Shahid Rajaee Teacher Training
University, Iran
Shahid Rajaee Teacher Training
University, Iran
AUTHOR
ORIGINAL_ARTICLE
Sharp Bounds on the PI Spectral Radius
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.
http://ijmc.kashanu.ac.ir/article_5141_706f04cbcca81707a324490ab2279fde.pdf
2010-04-01T11:23:20
2020-02-22T11:23:20
111
117
10.22052/ijmc.2010.5141
PI Matrix
PI Energy
PI Spectral Radius
M.
NADJAFI-ARANI
true
1
University of Kashan, I. R. Iran
University of Kashan, I. R. Iran
University of Kashan, I. R. Iran
AUTHOR
G.
FATH-TABAR
true
2
University of Kashan, I. R. Iran
University of Kashan, I. R. Iran
University of Kashan, I. R. Iran
AUTHOR
M.
MIRZARGAR
true
3
University of Kashan, I. R. Iran
University of Kashan, I. R. Iran
University of Kashan, I. R. Iran
AUTHOR
ORIGINAL_ARTICLE
Computation of Co-PI Index of TUC4C8(R) Nanotubes
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.
http://ijmc.kashanu.ac.ir/article_5142_619e84597c93a403ee5b4b0eaff4e4c0.pdf
2010-04-01T11:23:20
2020-02-22T11:23:20
119
123
10.22052/ijmc.2010.5142
Vertex-PI index
Co-PI index
TUC4C8 (R )Nanotube
F.
HASSANI
true
1
Payame Noor University, PNU Central Branch, Iran
Payame Noor University, PNU Central Branch, Iran
Payame Noor University, PNU Central Branch, Iran
AUTHOR
O.
KHORMALI
true
2
Tarbiat Modares University, Iran
Tarbiat Modares University, Iran
Tarbiat Modares University, Iran
AUTHOR
A.
IRANMANESH
true
3
Tarbiat Modares University,
Iran
Tarbiat Modares University,
Iran
Tarbiat Modares University,
Iran
AUTHOR
ORIGINAL_ARTICLE
Computing Vertex PI Index of Tetrathiafulvalene Dendrimers
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.
http://ijmc.kashanu.ac.ir/article_5143_7540ba516f7760926af890460197ac45.pdf
2010-04-01T11:23:20
2020-02-22T11:23:20
125
130
10.22052/ijmc.2010.5143
Dendrimer nanostar
PIv index
H.
SHABANI
true
1
University of Kashan, I. R. Iran
University of Kashan, I. R. Iran
University of Kashan, I. R. Iran
AUTHOR
ORIGINAL_ARTICLE
Computing PI and Hyper–Wiener Indices of Corona Product of some Graphs
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.
http://ijmc.kashanu.ac.ir/article_5144_046652966c70f5ddcb1c002144947c5b.pdf
2010-04-01T11:23:20
2020-02-22T11:23:20
131
135
10.22052/ijmc.2010.5144
Topological indices
PI index
Hyper−Wiener index
Wiener index
M.
TAVAKOLI
true
1
University of Tehran,
Islamic Republic of Iran
University of Tehran,
Islamic Republic of Iran
University of Tehran,
Islamic Republic of Iran
AUTHOR
H.
YOUSEFI–AZARI
true
2
University of Tehran,
Islamic Republic of Iran
University of Tehran,
Islamic Republic of Iran
University of Tehran,
Islamic Republic of Iran
AUTHOR