University of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)20100401Padmakar V Khadikar-Curriculum Vitae16512710.22052/ijmc.2010.5127ENM. V.DIUDEABabes-Bolyai University, Cluj, RomaniaA. D.ManikpuriDept. of Chemistry, IPS Academy, Indore-452010, MP, IndiaS. KarmarkarDept. of Chemistry, IPS Academy, Indore-452010, MP, IndiaJournal Article20090901University of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)20100401Padmakar-Ivan Index in Nanotechnology742513310.22052/ijmc.2010.5133ENP. V.KHADIKARKhatipura,
IndiaJournal Article20140420In 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.University of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)20100401Comparison of Topological Indices Based on Iterated ‘Sum’ versus ‘Product’ Operations4367513410.22052/ijmc.2010.5134ENA. T.BALABANTexas A&M University at Galveston, USAP. V.KHADIKARKhatipura, Indore
IndiaS. AZIZInstitute of Engineering and Technology, IndiaJournal Article20140420The 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.University of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)20100401Omega Polynomial in All R[8] Lattices6977513510.22052/ijmc.2010.5135ENM. V.DIUDEA“Babes-Bolyai” University, Cluj,
RomaniaJournal Article20140420Omega 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.University of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)20100401Computation of the Sadhana (Sd) Index of Linear Phenylenes and Corresponding Hexagonal Sequences7990513710.22052/ijmc.2010.5137ENS. AZIZInstitute of Engineering and Technology,
IndiaA. D.MANIKPURIIPS Academy, IndiaP. E.JOHNTechnische Universitat Iimenau, IlmenauP. KHADIKARKhatipura,
IndiaJournal Article20140420The 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.University of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)20100401Use of Structure Codes (Counts) for Computing Topological Indices of Carbon Nanotubes: Sadhana (Sd) Index of Phenylenes and its Hexagonal Squeezes9194513810.22052/ijmc.2010.5138ENP. E.JOHNTechnische Universitat Iimenau, IlmenauS. AZIZDepartment of Applied Sciences (Mathematics), IndoreP. V.KHADIKARLaxmi Fumigation and Pest Control, Khatipura, India.Journal Article20140420Structural 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.University of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)20100401Second and Third Extremals of Catacondensed Hexagonal Systems with Respect to the PI Index95103513910.22052/ijmc.2010.5139ENZ. YARAHMADIIslamic Azad University, Khorramabad Branch,
I. R. IranS. MORADIArak University, IranJournal Article20140420The 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.University of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)20100401Computing Vertex PI, Omega and Sadhana Polynomials of F12(2n+1) Fullerenes105110514010.22052/ijmc.2010.5140ENM. GHORBANIShahid Rajaee Teacher Training
University, IranJournal Article20140420The 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.University of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)20100401Sharp Bounds on the PI Spectral Radius111117514110.22052/ijmc.2010.5141ENM. J.NADJAFI-ARANIUniversity of Kashan, I. R. IranG. H.FATH-TABARUniversity of Kashan, I. R. IranM. MIRZARGARUniversity of Kashan, I. R. IranJournal Article20140420In 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.University of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)20100401Computation of Co-PI Index of TUC4C8(R) Nanotubes119123514210.22052/ijmc.2010.5142ENF. HASSANIPayame Noor University, PNU Central Branch, IranO. KHORMALITarbiat Modares University, IranA. IRANMANESHTarbiat Modares University,
IranJournal Article20140420In 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.University of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)20100401Computing Vertex PI Index of Tetrathiafulvalene Dendrimers125130514310.22052/ijmc.2010.5143ENH. SHABANIUniversity of Kashan, I. R. IranJournal Article20140420General 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.University of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 1 (Special Issue on the Role of PI Index in Nanotechnology)20100401Computing PI and Hyper–Wiener Indices of Corona Product of some Graphs131135514410.22052/ijmc.2010.5144ENM. TAVAKOLIUniversity of Tehran,
Islamic Republic of IranH. YOUSEFI–AZARIUniversity of Tehran,
Islamic Republic of IranJournal Article20140420Let 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.