University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 1 Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry) 2010 04 01 Autobiography of IVAN GUTMAN 1 4 5128 10.22052/ijmc.2010.5128 EN I. GUTMAN University of Kragujevac, Serbia Journal Article 2010 05 01 https://ijmc.kashanu.ac.ir/article_5128_025fbe1e83d02f1fe8cb43b602da986f.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 1 Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry) 2010 04 01 Wiener Way to Dimensionality 5 15 5150 10.22052/ijmc.2010.5150 EN O. ORI Via Casilina, Italy F. CATALDO Via Casilina, Italy D. VUKIČEVIĆ University of Split, Croatia A GRAOVAC The R. Bošković Institute”, Croatia Journal Article 2014 04 22 This 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. Wiener dimensionality Sierpinski fractals Asymptotic Wiener index https://ijmc.kashanu.ac.ir/article_5150_6de0a526852fe0f62c2951d4172451bd.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 1 Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry) 2010 04 01 On Second Geometric-Arithmetic Index of Graphs 17 28 5151 10.22052/ijmc.2010.5151 EN K. CH. DAS Sungkyunkwan University, Republic of Korea I. GUTMAN University of Kragujevac, Serbia B. FURTULA University of Kragujevac, Serbia Journal Article 2014 04 22 The 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. Graph Molecular Graph First geometric-arithmetic index Second geometric-arithmetic index Third geometric-arithmetic index https://ijmc.kashanu.ac.ir/article_5151_d31456f9d3923786c6852def2bdb8952.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 1 Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry) 2010 04 01 On Third Geometric-Arithmetic Index of Graphs 29 36 5152 10.22052/ijmc.2010.5152 EN K. CH. DAS Sungkyunkwan University, Republic of Korea I. GUTMAN University of Kragujevac, Serbia B. FURTULA University of Kragujevac, Serbia Journal Article 2014 04 22 Continuing 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. Graph Molecular Graph First geometric-arithmetic index Second geometric-arithmetic index Third geometric-arithmetic index https://ijmc.kashanu.ac.ir/article_5152_3f8b39102961616b12e394cdfc51c919.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 1 Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry) 2010 04 01 Some New Results On the Hosoya Polynomial of Graph Operations 37 43 5153 10.22052/ijmc.2010.5153 EN H. MOHAMADINEZHAD-RASHTI University of Tehran, Tehran, I. R. Iran H. YOUSEFI-AZARI University of Tehran, Tehran, I. R. Iran Journal Article 2014 04 22 The 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), 959969] 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. Wiener index Wiener polynomial Graph operation https://ijmc.kashanu.ac.ir/article_5153_4a3a57fbc78171abaef207326e14b456.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 1 Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry) 2010 04 01 Eccentric Connectivity Index: Extremal Graphs and Values 45 56 5154 10.22052/ijmc.2010.5154 EN T. DOŠLIĆ University of Zagreb, CROATIA M. SAHELI University of Kashan, I. R. IRAN D. VUKIČEVIĆ University of Split , CROATIA Journal Article 2014 04 22 Eccentric 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. eccentric connectivity index Extremal graph https://ijmc.kashanu.ac.ir/article_5154_3596a800067167a2d76a24fda346d9f6.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 1 Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry) 2010 04 01 Some Topological Indices of Nanostar Dendrimers 57 65 5155 10.22052/ijmc.2010.5155 EN M. GHORBANI Shahid Rajaee Teacher Training University, I. R. Iran M. SONGHORI Shahid Rajaee Teacher Training University, I. R. Iran Journal Article 2014 04 22 Wiener 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. Wiener index Szeged index Randić index Zagreb index ABC Index GA Index Nanostar dendrimers https://ijmc.kashanu.ac.ir/article_5155_001f28821a3446f33adf6f54093b73d1.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 1 Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry) 2010 04 01 Some Lower Bounds for Estrada Index 67 72 5156 10.22052/ijmc.2010.5156 EN B. ZHOU South China Normal University, China Z. DU South China Normal University, China Journal Article 2014 04 22 Estrada index Eigenvalues (of graph) Spectral moments Lower bounds https://ijmc.kashanu.ac.ir/article_5156_b5abf6a21ef9191afd2ed2ed0e250726.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 1 Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry) 2010 04 01 Topological Compression Factors of 2-Dimensional TUC4C8(R) Lattices and Tori 73 80 5157 10.22052/ijmc.2010.5157 EN T. DOŠLIĆ University of Zagreb, Croatia A. GRAOVAC The “Ruđer Bošković” Institute, Croatia D. VUKIČEVIĆ University of Split, Croatia F. CATALDO Actinium Chemical Research, Via Casilina , Italy O. ORI Actinium Chemical Research, Via Casilina Italy A. IRANMANESH Tarbiat Modaress University, Tehran, Iran A. R. ASHRAFI University of Kashan, Iran F. K. MOFTAKHAR University of Kashan, Iran Journal Article 2014 04 22 We 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-->∞. 2-Dimensional square-octagonal lattice eccentric connectivity index Wiener index Topological compression factors https://ijmc.kashanu.ac.ir/article_5157_980a8f6666ab80bbd1230e6d506def34.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 1 Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry) 2010 04 01 A Fast Approach to the Detection of All-Purpose Hubs in Complex Networks with Chemical Applications 81 96 5158 10.22052/ijmc.2010.5158 EN S. M. RAJTMAJER University of Dubrovnik, Croatia D. VUKIČEVIĆ University of Split, Croatia Journal Article 2014 04 22 A 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. Chemical networks Complex networks Network hubs Vertex centrality https://ijmc.kashanu.ac.ir/article_5158_e7348974c9083c796030f1b6bcb9a040.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 1 Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry) 2010 04 01 On General Sum-Connectivity Index of Benzenoid Systems and Phenylenes 97 104 5159 10.22052/ijmc.2010.5159 EN SH. CHEN Hunan City University, P. R. China F. XIA Hunan City University, P. R. China J. YANG Hunan City University, P. R. China Journal Article 2014 04 22 General sum-connectivity index Benzenoid systems Phenylene Hexagonal squeeze https://ijmc.kashanu.ac.ir/article_5159_e8c14ffd3fcc72860fec6d79779a6925.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 1 Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry) 2010 04 01 Eccentric Connectivity and Augmented Eccentric Connectivity Indices of N-Branched Phenylacetylenes Nanostar Dendrimers 105 110 5160 10.22052/ijmc.2010.5160 EN Z. YARAHMADI Islamic Azad University, Khorramabad Branch, I. R. Iran Journal Article 2014 04 22 eccentric connectivity index Augmented eccentric connectivity index Nanostar https://ijmc.kashanu.ac.ir/article_5160_dc269a19d114002da7214c9b5a03f9fc.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 1 Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry) 2010 04 01 Some Topological Indices of Tetrameric 1,3-Adamantane 111 118 5161 10.22052/ijmc.2010.5161 EN G. H. FATH–TABAR University of Kashan, I R. Iran A. AZAD Arak University, I. R. Iran N. ELAHINEZHAD Arak University, I. R. Iran Journal Article 2014 04 22 Topological 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. PI index Szeged index Zagreb index Tetrameric 1 3–adamatane https://ijmc.kashanu.ac.ir/article_5161_8e599d8a71d9221245ea807ae9e49da8.pdf