University of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)20100401Autobiography of IVAN GUTMAN14512810.22052/ijmc.2010.5128ENI.GUTMANUniversity of Kragujevac, SerbiaJournal Article20100501http://ijmc.kashanu.ac.ir/article_5128_025fbe1e83d02f1fe8cb43b602da986f.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)20100401Wiener Way to Dimensionality515515010.22052/ijmc.2010.5150ENO.ORIVia Casilina, ItalyF.CATALDOVia Casilina, ItalyD.VUKIČEVIĆUniversity of Split, CroatiaAGRAOVACThe R. Bošković Institute”, CroatiaJournal Article20140422This note introduces a new general conjecture correlating the dimensionality dT of an infinite lattice with N nodes to the asymptotic value of its Wiener Index W(N). In the limit of large N the general asymptotic behavior W(N)≈Ns is proposed, where the exponent s and dT are related by the conjectured formula s=2+1/dT allowing a new definition of dimensionality dW=(s-2)-1. Being related to the topological Wiener index, dW is therefore called Wiener dimensionality. Successful applications of this method to various infinite lattices (like graphene, nanocones, Sierpinski fractal triangle and carpet) testify the validity of the conjecture for infinite lattices.http://ijmc.kashanu.ac.ir/article_5150_6de0a526852fe0f62c2951d4172451bd.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)20100401On Second Geometric-Arithmetic Index of Graphs1728515110.22052/ijmc.2010.5151ENK. CH.DASSungkyunkwan University, Republic of
KoreaI.GUTMANUniversity of Kragujevac, SerbiaB.FURTULAUniversity of Kragujevac, SerbiaJournal Article20140422The concept of geometric-arithmetic indices (GA) was put forward in chemical graph theory very recently. In spite of this, several works have already appeared dealing with these indices. In this paper we present lower and upper bounds on the second geometric-arithmetic index (GA2) and characterize the extremal graphs. Moreover, we establish Nordhaus-Gaddum-type results for GA2.http://ijmc.kashanu.ac.ir/article_5151_d31456f9d3923786c6852def2bdb8952.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)20100401On Third Geometric-Arithmetic Index of Graphs2936515210.22052/ijmc.2010.5152ENK. CH.DASSungkyunkwan University, Republic of
KoreaI.GUTMANUniversity of Kragujevac, SerbiaB.FURTULAUniversity of Kragujevac, SerbiaJournal Article20140422Continuing the work K. C. Das, I. Gutman, B. Furtula, On second geometric-arithmetic index of graphs, Iran. J. Math Chem., 1(2) (2010) 17-28, in this paper we present lower and upper bounds on the third geometric-arithmetic index GA3 and characterize the extremal graphs. Moreover, we give Nordhaus-Gaddum-type result for GA3.http://ijmc.kashanu.ac.ir/article_5152_3f8b39102961616b12e394cdfc51c919.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)20100401Some New Results On the Hosoya Polynomial of Graph Operations3743515310.22052/ijmc.2010.5153ENH.MOHAMADINEZHAD-RASHTIUniversity of Tehran, Tehran,
I. R. IranH.YOUSEFI-AZARIUniversity of Tehran, Tehran,
I. R. IranJournal Article20140422The Wiener index is a graph invariant that has found extensive application in chemistry. In addition to that a generating function, which was called the Wiener polynomial, who’s derivate is a q-analog of the Wiener index was defined. In an article, Sagan, Yeh and Zhang in [The Wiener Polynomial of a graph, Int. J. Quantun Chem., 60 (1996), 959969] attained what graph operations do to the Wiener polynomial. By considering all the results that Sagan et al. admitted for Wiener polynomial on graph operations for each two connected and nontrivial graphs, in this article we focus on deriving Wiener polynomial of graph operations, Join, Cartesian product, Composition, Disjunction and Symmetric difference on n graphs and Wiener indices of them.http://ijmc.kashanu.ac.ir/article_5153_4a3a57fbc78171abaef207326e14b456.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)20100401Eccentric Connectivity Index: Extremal Graphs and Values4556515410.22052/ijmc.2010.5154ENT.DOŠLIĆUniversity of Zagreb,
CROATIAM.SAHELIUniversity of Kashan,
I. R. IRAND.VUKIČEVIĆUniversity of Split , CROATIAJournal Article20140422Eccentric connectivity index has been found to have a low degeneracy and hence a significant potential of predicting biological activity of certain classes of chemical compounds. We present here explicit formulas for eccentric connectivity index of various families of graphs. We also show that the eccentric connectivity index grows at most polynomially with the number of vertices and determine the leading coefficient in the asymptotic behavior.http://ijmc.kashanu.ac.ir/article_5154_3596a800067167a2d76a24fda346d9f6.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)20100401Some Topological Indices of Nanostar Dendrimers5765515510.22052/ijmc.2010.5155ENM.GHORBANIShahid Rajaee Teacher Training
University, I. R. IranM.SONGHORIShahid Rajaee Teacher Training
University, I. R. IranJournal Article20140422Wiener index is a topological index based on distance between every pair of vertices in a graph G. It was introduced in 1947 by one of the pioneer of this area e.g, Harold Wiener. In the present paper, by using a new method introduced by klavžar we compute the Wiener and Szeged indices of some nanostar dendrimers.http://ijmc.kashanu.ac.ir/article_5155_001f28821a3446f33adf6f54093b73d1.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)20100401Some Lower Bounds for Estrada Index6772515610.22052/ijmc.2010.5156ENB.ZHOUSouth China Normal University, ChinaZ.DUSouth China Normal University, ChinaJournal Article20140422http://ijmc.kashanu.ac.ir/article_5156_b5abf6a21ef9191afd2ed2ed0e250726.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)20100401Topological Compression Factors of 2-Dimensional TUC4C8(R) Lattices and Tori7380515710.22052/ijmc.2010.5157ENT.DOŠLIĆUniversity of Zagreb,
CroatiaA.GRAOVACThe “Ruđer Bošković” Institute, CroatiaD.VUKIČEVIĆUniversity of Split, CroatiaF.CATALDOActinium Chemical Research, Via Casilina , ItalyO.ORIActinium Chemical Research, Via Casilina ItalyA.IRANMANESHTarbiat Modaress University, Tehran, IranA. R.ASHRAFIUniversity of Kashan, IranF. K.MOFTAKHARUniversity of Kashan, IranJournal Article20140422We derived explicit formulae for the eccentric connectivity index and Wiener index of 2-dimensional square-octagonal TUC4C8(R) lattices with open and closed ends. New compression factors for both indices are also computed in the limit N-->∞.http://ijmc.kashanu.ac.ir/article_5157_980a8f6666ab80bbd1230e6d506def34.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)20100401A Fast Approach to the Detection of All-Purpose Hubs in Complex Networks with Chemical Applications8196515810.22052/ijmc.2010.5158ENS. M.RAJTMAJERUniversity of Dubrovnik, CroatiaD.VUKIČEVIĆUniversity of Split, CroatiaJournal Article20140422A novel algorithm for the fast detection of hubs in chemical networks is presented. The algorithm identifies a set of nodes in the network as most significant, aimed to be the most effective points of distribution for fast, widespread coverage throughout the system. We show that our hubs have in general greater closeness centrality and betweenness centrality than vertices with maximal degree, while having comparable or higher degree than vertices with greatest closeness centrality and betweenness centrality. As such, they serve as all-purpose network hubs. Several theoretical and real world chemical and biological networks are tested and results are analyzed.http://ijmc.kashanu.ac.ir/article_5158_e7348974c9083c796030f1b6bcb9a040.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)20100401On General Sum-Connectivity Index of Benzenoid Systems and Phenylenes97104515910.22052/ijmc.2010.5159ENSH.CHENHunan City University, P. R. ChinaF.XIAHunan City University, P. R. ChinaJ.YANGHunan City University, P. R. ChinaJournal Article20140422http://ijmc.kashanu.ac.ir/article_5159_e8c14ffd3fcc72860fec6d79779a6925.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)20100401Eccentric Connectivity and Augmented Eccentric Connectivity Indices of N-Branched Phenylacetylenes Nanostar Dendrimers105110516010.22052/ijmc.2010.5160ENZ.YARAHMADIIslamic Azad University, Khorramabad Branch,
I. R. IranJournal Article20140422http://ijmc.kashanu.ac.ir/article_5160_dc269a19d114002da7214c9b5a03f9fc.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64891Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)20100401Some Topological Indices of Tetrameric 1,3-Adamantane111118516110.22052/ijmc.2010.5161ENG. H.FATH–TABARUniversity of Kashan, I R. IranA.AZADArak University,
I. R. IranN.ELAHINEZHADArak University,
I. R. IranJournal Article20140422Topological indices are numerical parameters of a graph which characterize its topology. In this paper the PI, Szeged and Zagreb group indices of the tetrameric 1,3–adamantane are computed.http://ijmc.kashanu.ac.ir/article_5161_8e599d8a71d9221245ea807ae9e49da8.pdf