2010
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Padmakar V KhadikarCurriculum Vitae
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M.
DIUDEA
BabesBolyai University, Cluj, Romania
BabesBolyai University, Cluj, Romania
Romania
diudea@gmail.com


A.
Manikpuri
Dept. of Chemistry, IPS Academy, Indore452010, MP, India
Dept. of Chemistry, IPS Academy, Indore452010,
Iran


S.
Karmarkar
Dept. of Chemistry, IPS Academy, Indore452010, MP, India
Dept. of Chemistry, IPS Academy, Indore452010,
Iran
PadmakarIvan Index in Nanotechnology
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In this survey article a brief account on the development of PadmakarIvan (PI) index in that applications of PadmakarIvan (PI) index in the fascinating field of nanotechnology are discussed.
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7
42


P.
KHADIKAR
Khatipura,
India
Khatipura,
India
India
Padmakar−Ivan index
Topological index
Carbon nanotubes
Nanotechnology
Comparison of Topological Indices Based on Iterated ‘Sum’ versus ‘Product’ Operations
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2
The PadmakarIvan (PI) index is a firstgeneration 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 hydrogendepleted graph.
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43
67


A.
BALABAN
Texas A&M University at Galveston, USA
Texas A&M University at Galveston, USA
USA


P.
KHADIKAR
Khatipura, Indore
India
Khatipura, Indore
India
India


S.
AZIZ
Institute of Engineering and Technology, India
Institute of Engineering and Technology,
India
Topological indices
PI index
Balaban index J
Wiener index W
F and G indices
Omega Polynomial in All R[8] Lattices
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2
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 ClujIlmenau 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.
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69
77


M.
DIUDEA
“BabesBolyai” University, Cluj,
Romania
“BabesBolyai” University, Cluj,
Roman
Romania
Omega polynomial
Dyck graph
Lattice, Map operations
Computation of the Sadhana (Sd) Index of Linear Phenylenes and Corresponding Hexagonal Sequences
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2
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.
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79
90


S.
AZIZ
Institute of Engineering and Technology,
India
Institute of Engineering and Technology,
India


A.
MANIKPURI
IPS Academy, India
IPS Academy, India
India


P.
JOHN
Technische Universitat Iimenau, Ilmenau
Technische Universitat Iimenau, Ilmenau
Germany


P.
KHADIKAR
Khatipura,
India
Khatipura,
India
India
Sd index
PI index
Phenylenes
Hexagonal chain
Use of Structure Codes (Counts) for Computing Topological Indices of Carbon Nanotubes: Sadhana (Sd) Index of Phenylenes and its Hexagonal Squeezes
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2
Structural codes visavis structural counts, like polynomials of a molecular graph, are important in computing graphtheoretical 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 WSzPItype 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 PIindices.
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91
94


P.
JOHN
Technische Universitat Iimenau, Ilmenau
Technische Universitat Iimenau, Ilmenau
Germany


S.
AZIZ
Department of Applied Sciences (Mathematics), Indore
Department of Applied Sciences (Mathematics),
India


P.
KHADIKAR
Laxmi Fumigation and Pest Control, Khatipura, India.
Laxmi Fumigation and Pest Control, Khatipura,
India
Sadhana index
Graphtheoretical descriptor
Structural codes
Structural counts phenylene
Hexagonal squeeze
Benzenoids
Second and Third Extremals of Catacondensed Hexagonal Systems with Respect to the PI Index
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2
The PadmakarIvan (PI) index is a WienerSzegedlike 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.
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95
103


Z.
YARAHMADI
Islamic Azad University, Khorramabad Branch,
I. R. Iran
Islamic Azad University, Khorramabad Branch,
I.
I R Iran


S.
MORADI
Arak University, Iran
Arak University, Iran
I R Iran
Topological index
PI index
Catacondensed hexagonal system
Computing Vertex PI, Omega and Sadhana Polynomials of F12(2n+1) Fullerenes
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2
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.
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105
110


M.
GHORBANI
Shahid Rajaee Teacher Training
University, Iran
Shahid Rajaee Teacher Training
University,
I R Iran
Fullerene
Vertex PI polynomial
Omega polynomial
Sadhana polynomial
Sharp Bounds on the PI Spectral Radius
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2
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.
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111
117


M.
NADJAFIARANI
University of Kashan, I. R. Iran
University of Kashan, I. R. Iran
I R Iran


G.
FATHTABAR
University of Kashan, I. R. Iran
University of Kashan, I. R. Iran
I R Iran


M.
MIRZARGAR
University of Kashan, I. R. Iran
University of Kashan, I. R. Iran
I R Iran
PI Matrix
PI Energy
PI Spectral Radius
Computation of CoPI Index of TUC4C8(R) Nanotubes
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2
In this paper, at first we introduce a new index with the name CoPI index and obtain some properties related this new index. Then we compute this new index for TUC4C8(R) nanotubes.
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119
123


F.
HASSANI
Payame Noor University, PNU Central Branch, Iran
Payame Noor University, PNU Central Branch,
I R Iran


O.
KHORMALI
Tarbiat Modares University, Iran
Tarbiat Modares University, Iran
I R Iran


A.
IRANMANESH
Tarbiat Modares University,
Iran
Tarbiat Modares University,
Iran
I R Iran
VertexPI index
CoPI index
TUC4C8 (R )Nanotube
Computing Vertex PI Index of Tetrathiafulvalene Dendrimers
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2
General formulas are obtained for the vertex PadmakarIvan index (PIv) of tetrathiafulvalene (TTF) dendrimer, whereby TTF units we are employed as branching centers. The PIv index is a WienerSzegedlike 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.
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125
130


H.
SHABANI
University of Kashan, I. R. Iran
University of Kashan, I. R. Iran
I R Iran
Dendrimer nanostar
PIv index
Computing PI and Hyper–Wiener Indices of Corona Product of some Graphs
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2
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 ith copy of H to the ith vertex of G, i = 1, 2, …, V(G). In this paper, we compute PI and hyper–Wiener indices of the corona product of graphs.
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131
135


M.
TAVAKOLI
University of Tehran,
Islamic Republic of Iran
University of Tehran,
Islamic Republic of
I R Iran


H.
YOUSEFI–AZARI
University of Tehran,
Islamic Republic of Iran
University of Tehran,
Islamic Republic of
I R Iran
Topological indices
PI index
Hyper−Wiener index
Wiener index