@article {
author = {DIUDEA, M. and Manikpuri, A. and Karmarkar, S.},
title = {Padmakar V Khadikar-Curriculum Vitae},
journal = {Iranian Journal of Mathematical Chemistry},
volume = {1},
number = {Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)},
pages = {1-6},
year = {2010},
publisher = {University of Kashan},
issn = {2228-6489},
eissn = {2008-9015},
doi = {10.22052/ijmc.2010.5127},
abstract = {},
keywords = {},
url = {https://ijmc.kashanu.ac.ir/article_5127.html},
eprint = {https://ijmc.kashanu.ac.ir/article_5127_614a7ce8bd9a6e3ae333ee471d0696a3.pdf}
}
@article {
author = {KHADIKAR, P.},
title = {Padmakar-Ivan Index in Nanotechnology},
journal = {Iranian Journal of Mathematical Chemistry},
volume = {1},
number = {Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)},
pages = {7-42},
year = {2010},
publisher = {University of Kashan},
issn = {2228-6489},
eissn = {2008-9015},
doi = {10.22052/ijmc.2010.5133},
abstract = {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.},
keywords = {Padmakar−Ivan index,topological index,Carbon nanotubes,Nanotechnology},
url = {https://ijmc.kashanu.ac.ir/article_5133.html},
eprint = {https://ijmc.kashanu.ac.ir/article_5133_69608829fde8da3739d297fe668c4e85.pdf}
}
@article {
author = {BALABAN, A. and KHADIKAR, P. and AZIZ, S.},
title = {Comparison of Topological Indices Based on Iterated ‘Sum’ versus ‘Product’ Operations},
journal = {Iranian Journal of Mathematical Chemistry},
volume = {1},
number = {Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)},
pages = {43-67},
year = {2010},
publisher = {University of Kashan},
issn = {2228-6489},
eissn = {2008-9015},
doi = {10.22052/ijmc.2010.5134},
abstract = {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.},
keywords = {Topological indices,PI index,Balaban index J,Wiener index W,F and G indices},
url = {https://ijmc.kashanu.ac.ir/article_5134.html},
eprint = {https://ijmc.kashanu.ac.ir/article_5134_d70fc0d453920cc63e95881e6835da9e.pdf}
}
@article {
author = {DIUDEA, M.},
title = {Omega Polynomial in All R[8] Lattices},
journal = {Iranian Journal of Mathematical Chemistry},
volume = {1},
number = {Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)},
pages = {69-77},
year = {2010},
publisher = {University of Kashan},
issn = {2228-6489},
eissn = {2008-9015},
doi = {10.22052/ijmc.2010.5135},
abstract = {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.},
keywords = {Omega polynomial,Dyck graph,Lattice, Map operations},
url = {https://ijmc.kashanu.ac.ir/article_5135.html},
eprint = {https://ijmc.kashanu.ac.ir/article_5135_463c4d3a0e2258ddb04ccb6462bc892c.pdf}
}
@article {
author = {AZIZ, S. and MANIKPURI, A. and JOHN, P. and KHADIKAR, P.},
title = {Computation of the Sadhana (Sd) Index of Linear Phenylenes and Corresponding Hexagonal Sequences},
journal = {Iranian Journal of Mathematical Chemistry},
volume = {1},
number = {Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)},
pages = {79-90},
year = {2010},
publisher = {University of Kashan},
issn = {2228-6489},
eissn = {2008-9015},
doi = {10.22052/ijmc.2010.5137},
abstract = {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.},
keywords = {Sd index,PI index,Phenylenes,Hexagonal chain},
url = {https://ijmc.kashanu.ac.ir/article_5137.html},
eprint = {https://ijmc.kashanu.ac.ir/article_5137_77cc2337e6077e5017bd6b709c9e11c1.pdf}
}
@article {
author = {JOHN, P. and AZIZ, S. and KHADIKAR, P.},
title = {Use of Structure Codes (Counts) for Computing Topological Indices of Carbon Nanotubes: Sadhana (Sd) Index of Phenylenes and its Hexagonal Squeezes},
journal = {Iranian Journal of Mathematical Chemistry},
volume = {1},
number = {Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)},
pages = {91-94},
year = {2010},
publisher = {University of Kashan},
issn = {2228-6489},
eissn = {2008-9015},
doi = {10.22052/ijmc.2010.5138},
abstract = {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.},
keywords = {Sadhana index,Graph-theoretical descriptor,Structural codes,Structural counts phenylene,Hexagonal squeeze,Benzenoids},
url = {https://ijmc.kashanu.ac.ir/article_5138.html},
eprint = {https://ijmc.kashanu.ac.ir/article_5138_27ded09e0fb14ea6a65bfd0082c84828.pdf}
}
@article {
author = {YARAHMADI, Z. and MORADI, S.},
title = {Second and Third Extremals of Catacondensed Hexagonal Systems with Respect to the PI Index},
journal = {Iranian Journal of Mathematical Chemistry},
volume = {1},
number = {Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)},
pages = {95-103},
year = {2010},
publisher = {University of Kashan},
issn = {2228-6489},
eissn = {2008-9015},
doi = {10.22052/ijmc.2010.5139},
abstract = {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.},
keywords = {topological index,PI index,Catacondensed hexagonal system},
url = {https://ijmc.kashanu.ac.ir/article_5139.html},
eprint = {https://ijmc.kashanu.ac.ir/article_5139_1102d2fd97f933fa29079d6446627c4e.pdf}
}
@article {
author = {GHORBANI, M.},
title = {Computing Vertex PI, Omega and Sadhana Polynomials of F12(2n+1) Fullerenes},
journal = {Iranian Journal of Mathematical Chemistry},
volume = {1},
number = {Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)},
pages = {105-110},
year = {2010},
publisher = {University of Kashan},
issn = {2228-6489},
eissn = {2008-9015},
doi = {10.22052/ijmc.2010.5140},
abstract = {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.},
keywords = {Fullerene,Vertex PI polynomial,Omega polynomial,Sadhana polynomial},
url = {https://ijmc.kashanu.ac.ir/article_5140.html},
eprint = {https://ijmc.kashanu.ac.ir/article_5140_2a8c232a74e722a17ed57f7a0a5fc608.pdf}
}
@article {
author = {NADJAFI-ARANI, M. and FATH-TABAR, G. and MIRZARGAR, M.},
title = {Sharp Bounds on the PI Spectral Radius},
journal = {Iranian Journal of Mathematical Chemistry},
volume = {1},
number = {Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)},
pages = {111-117},
year = {2010},
publisher = {University of Kashan},
issn = {2228-6489},
eissn = {2008-9015},
doi = {10.22052/ijmc.2010.5141},
abstract = {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.},
keywords = {PI Matrix,PI Energy,PI Spectral Radius},
url = {https://ijmc.kashanu.ac.ir/article_5141.html},
eprint = {https://ijmc.kashanu.ac.ir/article_5141_706f04cbcca81707a324490ab2279fde.pdf}
}
@article {
author = {HASSANI, F. and KHORMALI, O. and IRANMANESH, A.},
title = {Computation of Co-PI Index of TUC4C8(R) Nanotubes},
journal = {Iranian Journal of Mathematical Chemistry},
volume = {1},
number = {Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)},
pages = {119-123},
year = {2010},
publisher = {University of Kashan},
issn = {2228-6489},
eissn = {2008-9015},
doi = {10.22052/ijmc.2010.5142},
abstract = {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.},
keywords = {Vertex-PI index,Co-PI index,TUC4C8 (R )Nanotube},
url = {https://ijmc.kashanu.ac.ir/article_5142.html},
eprint = {https://ijmc.kashanu.ac.ir/article_5142_619e84597c93a403ee5b4b0eaff4e4c0.pdf}
}
@article {
author = {SHABANI, H.},
title = {Computing Vertex PI Index of Tetrathiafulvalene Dendrimers},
journal = {Iranian Journal of Mathematical Chemistry},
volume = {1},
number = {Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)},
pages = {125-130},
year = {2010},
publisher = {University of Kashan},
issn = {2228-6489},
eissn = {2008-9015},
doi = {10.22052/ijmc.2010.5143},
abstract = {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.},
keywords = {Dendrimer nanostar,PIv index},
url = {https://ijmc.kashanu.ac.ir/article_5143.html},
eprint = {https://ijmc.kashanu.ac.ir/article_5143_7540ba516f7760926af890460197ac45.pdf}
}
@article {
author = {TAVAKOLI, M. and YOUSEFI–AZARI, H.},
title = {Computing PI and Hyper–Wiener Indices of Corona Product of some Graphs},
journal = {Iranian Journal of Mathematical Chemistry},
volume = {1},
number = {Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)},
pages = {131-135},
year = {2010},
publisher = {University of Kashan},
issn = {2228-6489},
eissn = {2008-9015},
doi = {10.22052/ijmc.2010.5144},
abstract = {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.},
keywords = {Topological indices,PI index,Hyper−Wiener index,Wiener index},
url = {https://ijmc.kashanu.ac.ir/article_5144.html},
eprint = {https://ijmc.kashanu.ac.ir/article_5144_046652966c70f5ddcb1c002144947c5b.pdf}
}