eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
1
6
10.22052/ijmc.2010.5127
5127
Padmakar V Khadikar-Curriculum Vitae
M. DIUDEA
diudea@gmail.com
1
A. Manikpuri
2
S. Karmarkar
3
Babes-Bolyai University, Cluj, Romania
Dept. of Chemistry, IPS Academy, Indore-452010, MP, India
Dept. of Chemistry, IPS Academy, Indore-452010, MP, India
https://ijmc.kashanu.ac.ir/article_5127_614a7ce8bd9a6e3ae333ee471d0696a3.pdf
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
7
42
10.22052/ijmc.2010.5133
5133
Padmakar-Ivan Index in Nanotechnology
P. KHADIKAR
1
Khatipura, India
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.
https://ijmc.kashanu.ac.ir/article_5133_69608829fde8da3739d297fe668c4e85.pdf
Padmakar−Ivan index
topological index
Carbon nanotubes
Nanotechnology
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
43
67
10.22052/ijmc.2010.5134
5134
Comparison of Topological Indices Based on Iterated ‘Sum’ versus ‘Product’ Operations
A. BALABAN
1
P. KHADIKAR
2
S. AZIZ
3
Texas A&M University at Galveston, USA
Khatipura, Indore India
Institute of Engineering and Technology, India
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.
https://ijmc.kashanu.ac.ir/article_5134_d70fc0d453920cc63e95881e6835da9e.pdf
Topological indices
PI index
Balaban index J
Wiener index W
F and G indices
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
69
77
10.22052/ijmc.2010.5135
5135
Omega Polynomial in All R[8] Lattices
M. DIUDEA
1
“Babes-Bolyai” University, Cluj, Romania
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.
https://ijmc.kashanu.ac.ir/article_5135_463c4d3a0e2258ddb04ccb6462bc892c.pdf
Omega polynomial
Dyck graph
Lattice, Map operations
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
79
90
10.22052/ijmc.2010.5137
5137
Computation of the Sadhana (Sd) Index of Linear Phenylenes and Corresponding Hexagonal Sequences
S. AZIZ
1
A. MANIKPURI
2
P. JOHN
3
P. KHADIKAR
4
Institute of Engineering and Technology, India
IPS Academy, India
Technische Universitat Iimenau, Ilmenau
Khatipura, India
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.
https://ijmc.kashanu.ac.ir/article_5137_77cc2337e6077e5017bd6b709c9e11c1.pdf
Sd index
PI index
Phenylenes
Hexagonal chain
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
91
94
10.22052/ijmc.2010.5138
5138
Use of Structure Codes (Counts) for Computing Topological Indices of Carbon Nanotubes: Sadhana (Sd) Index of Phenylenes and its Hexagonal Squeezes
P. JOHN
1
S. AZIZ
2
P. KHADIKAR
3
Technische Universitat Iimenau, Ilmenau
Department of Applied Sciences (Mathematics), Indore
Laxmi Fumigation and Pest Control, Khatipura, India.
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.
https://ijmc.kashanu.ac.ir/article_5138_27ded09e0fb14ea6a65bfd0082c84828.pdf
Sadhana index
Graph-theoretical descriptor
Structural codes
Structural counts phenylene
Hexagonal squeeze
Benzenoids
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
95
103
10.22052/ijmc.2010.5139
5139
Second and Third Extremals of Catacondensed Hexagonal Systems with Respect to the PI Index
Z. YARAHMADI
1
S. MORADI
2
Islamic Azad University, Khorramabad Branch, I. R. Iran
Arak University, Iran
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.
https://ijmc.kashanu.ac.ir/article_5139_1102d2fd97f933fa29079d6446627c4e.pdf
topological index
PI index
Catacondensed hexagonal system
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
105
110
10.22052/ijmc.2010.5140
5140
Computing Vertex PI, Omega and Sadhana Polynomials of F12(2n+1) Fullerenes
M. GHORBANI
1
Shahid Rajaee Teacher Training University, Iran
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.
https://ijmc.kashanu.ac.ir/article_5140_2a8c232a74e722a17ed57f7a0a5fc608.pdf
Fullerene
Vertex PI polynomial
Omega polynomial
Sadhana polynomial
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
111
117
10.22052/ijmc.2010.5141
5141
Sharp Bounds on the PI Spectral Radius
M. NADJAFI-ARANI
1
G. FATH-TABAR
2
M. MIRZARGAR
3
University of Kashan, I. R. Iran
University of Kashan, I. R. Iran
University of Kashan, I. R. Iran
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.
https://ijmc.kashanu.ac.ir/article_5141_706f04cbcca81707a324490ab2279fde.pdf
PI Matrix
PI Energy
PI Spectral Radius
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
119
123
10.22052/ijmc.2010.5142
5142
Computation of Co-PI Index of TUC4C8(R) Nanotubes
F. HASSANI
1
O. KHORMALI
2
A. IRANMANESH
3
Payame Noor University, PNU Central Branch, Iran
Tarbiat Modares University, Iran
Tarbiat Modares University, Iran
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.
https://ijmc.kashanu.ac.ir/article_5142_619e84597c93a403ee5b4b0eaff4e4c0.pdf
Vertex-PI index
Co-PI index
TUC4C8 (R )Nanotube
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
125
130
10.22052/ijmc.2010.5143
5143
Computing Vertex PI Index of Tetrathiafulvalene Dendrimers
H. SHABANI
1
University of Kashan, I. R. Iran
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.
https://ijmc.kashanu.ac.ir/article_5143_7540ba516f7760926af890460197ac45.pdf
Dendrimer nanostar
PIv index
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2010-04-01
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
131
135
10.22052/ijmc.2010.5144
5144
Computing PI and Hyper–Wiener Indices of Corona Product of some Graphs
M. TAVAKOLI
1
H. YOUSEFI–AZARI
2
University of Tehran, Islamic Republic of Iran
University of Tehran, Islamic Republic of Iran
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.
https://ijmc.kashanu.ac.ir/article_5144_046652966c70f5ddcb1c002144947c5b.pdf
Topological indices
PI index
Hyper−Wiener index
Wiener index