2020-08-09T09:36:12Z
https://ijmc.kashanu.ac.ir/?_action=export&rf=summon&issue=856
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
Padmakar V Khadikar-Curriculum Vitae
M.
DIUDEA
A.
Manikpuri
S.
Karmarkar
2010
04
01
1
6
https://ijmc.kashanu.ac.ir/article_5127_614a7ce8bd9a6e3ae333ee471d0696a3.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
Padmakar-Ivan Index in Nanotechnology
P.
KHADIKAR
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
2010
04
01
7
42
https://ijmc.kashanu.ac.ir/article_5133_69608829fde8da3739d297fe668c4e85.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
Comparison of Topological Indices Based on Iterated ‘Sum’ versus ‘Product’ Operations
A.
BALABAN
P.
KHADIKAR
S.
AZIZ
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
2010
04
01
43
67
https://ijmc.kashanu.ac.ir/article_5134_d70fc0d453920cc63e95881e6835da9e.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
Omega Polynomial in All R[8] Lattices
M.
DIUDEA
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
2010
04
01
69
77
https://ijmc.kashanu.ac.ir/article_5135_463c4d3a0e2258ddb04ccb6462bc892c.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
Computation of the Sadhana (Sd) Index of Linear Phenylenes and Corresponding Hexagonal Sequences
S.
AZIZ
A.
MANIKPURI
P.
JOHN
P.
KHADIKAR
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
2010
04
01
79
90
https://ijmc.kashanu.ac.ir/article_5137_77cc2337e6077e5017bd6b709c9e11c1.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
Use of Structure Codes (Counts) for Computing Topological Indices of Carbon Nanotubes: Sadhana (Sd) Index of Phenylenes and its Hexagonal Squeezes
P.
JOHN
S.
AZIZ
P.
KHADIKAR
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
2010
04
01
91
94
https://ijmc.kashanu.ac.ir/article_5138_27ded09e0fb14ea6a65bfd0082c84828.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
Second and Third Extremals of Catacondensed Hexagonal Systems with Respect to the PI Index
Z.
YARAHMADI
S.
MORADI
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
2010
04
01
95
103
https://ijmc.kashanu.ac.ir/article_5139_1102d2fd97f933fa29079d6446627c4e.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
Computing Vertex PI, Omega and Sadhana Polynomials of F12(2n+1) Fullerenes
M.
GHORBANI
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
2010
04
01
105
110
https://ijmc.kashanu.ac.ir/article_5140_2a8c232a74e722a17ed57f7a0a5fc608.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
Sharp Bounds on the PI Spectral Radius
M.
NADJAFI-ARANI
G.
FATH-TABAR
M.
MIRZARGAR
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
2010
04
01
111
117
https://ijmc.kashanu.ac.ir/article_5141_706f04cbcca81707a324490ab2279fde.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
Computation of Co-PI Index of TUC4C8(R) Nanotubes
F.
HASSANI
O.
KHORMALI
A.
IRANMANESH
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
2010
04
01
119
123
https://ijmc.kashanu.ac.ir/article_5142_619e84597c93a403ee5b4b0eaff4e4c0.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
Computing Vertex PI Index of Tetrathiafulvalene Dendrimers
H.
SHABANI
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
2010
04
01
125
130
https://ijmc.kashanu.ac.ir/article_5143_7540ba516f7760926af890460197ac45.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2010
1
Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)
Computing PI and Hyper–Wiener Indices of Corona Product of some Graphs
M.
TAVAKOLI
H.
YOUSEFI–AZARI
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
2010
04
01
131
135
https://ijmc.kashanu.ac.ir/article_5144_046652966c70f5ddcb1c002144947c5b.pdf