University of KashanIranian Journal of Mathematical Chemistry2228-64893220120901On Discriminativity of Vertex-degree-based Indices95101522410.22052/ijmc.2012.5224ENI.GUTMANUniversity of Kragujevac, Kragujevac, SerbiaJournal Article20140429A recently published paper [T. Došlić, this journal 3 (2012) 25-34] considers the Zagreb indices of benzenoid systems, and points out their low discriminativity. We show that analogous results hold for a variety of vertex-degree-based molecular structure descriptors that are being studied in contemporary mathematical chemistry. We also show that these results are straightforwardly obtained by using some identities, well known in the theory of benzenoid hydrocarbons.https://ijmc.kashanu.ac.ir/article_5224_cc384c68ad503482fb24e6d1e3b512ae.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64893220120901Computational and Electrochemical Studies on the Redox Reaction of 2-(2,3-Dihydroxy Phenyl)-1,3- Dithiane in Aqueous Solution103112522710.22052/ijmc.2012.5227ENM.MAZLOUM-ARDAKANIYazd University, I.R. IranH.BEITOLLAHIYazd University, I.R. IranH.FARROKHPOURIsfahan University of Technology, IranA. R.KHOSHROOIsfahan University of Technology, IranJournal Article20140429Electrode potential of 2-(2,3-dihydroxy phenyl)-1,3-dithiane (DPD) was investigated by means of cyclic voltammetry (CV) at various potential scan rates. The calculated value was compared with the experimental value obtained by cyclic voltammetry (CV). All experiments were done in aqueous phosphate buffer solutions at different pHs. The experimental redox potential of DPD was obtained to be 0.753 V versus SHE (Standard Hydrogen Electrode). DFT-B3LYP calculations using 6-311++G** basis set were performed to calculate the absolute redox potential of DPD. The calculated value of the redox potential relative to SHE is 0.766 V which is in good agreement with the experimental value (0.753).https://ijmc.kashanu.ac.ir/article_5227_b91f4f4d36fa98a94ac5584af95594a0.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64893220120901On the Tutte Polynomial of Benzenoid Chains113119522910.22052/ijmc.2012.5229ENG.FATH-TABARUniversity of Kashan,
I. R. IranZ.GHOLAM-REZAEIUniversity of Kashan,
I. R. IranA. R.ASHRAFIUniversity of Kashan,
I. R. IranJournal Article20140429The Tutte polynomial of a graph G, T(G, x,y) is a polynomial in two variables defined for every undirected graph contains information about how the graph is connected. In this paper a simple formula for computing Tutte polynomial of a benzenoid chain is presented.https://ijmc.kashanu.ac.ir/article_5229_080acdcce72c06873a773c4311c2e464.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64893220120901Computing Wiener and Hyper–Wiener Indices of Unitary Cayley Graphs121125523010.22052/ijmc.2012.5230ENA.LOGHMANPayame Noor Universtiy, IRANJournal Article20140429The unitary Cayley graph Xn has vertex set Zn = {0, 1,…, n-1} and vertices u and v are adjacent, if gcd(uv, n) = 1. In [A. Ilić, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881–1889], the energy of unitary Cayley graphs is computed. In this paper the Wiener and hyperWiener index of Xn is computed.https://ijmc.kashanu.ac.ir/article_5230_28b9f8aa9f07db88404721af4a5b6c11.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64893220120901Chromatic Polynomials of Some Nanostars127135523210.22052/ijmc.2012.5232ENS.ALIKHANIYazd University, IranM. A.IRANMANESHYazd University, Yazd, IranJournal Article20140429Let G be a simple graph and (G,) denotes the number of proper vertex colourings of G with at most colours, which is for a fixed graph G , a polynomial in , which is called the chromatic polynomial of G . Using the chromatic polynomial of some specific graphs, we obtain the chromatic polynomials of some nanostars.https://ijmc.kashanu.ac.ir/article_5232_067ee197a2aa979778923af77b40dd89.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64893220120901Note on Multiple Zagreb Indices137143523310.22052/ijmc.2012.5233ENM.GHORBANIShahid Rajaee Teacher Training
University, I. R. IranN.AZIMIShahid Rajaee Teacher Training
University, I. R. Iran;Journal Article20140429The Zagreb indices are the oldest graph invariants used in mathematical chemistry to predict the chemical phenomena. In this paper we define the multiple versions of Zagreb indices based on degrees of vertices in a given graph and then we compute the first and second extremal graphs for them.https://ijmc.kashanu.ac.ir/article_5233_26b58a41da329e0cbde0cbf956640a58.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64893220120901On Multiplicative Zagreb Indices of Graphs145154523410.22052/ijmc.2012.5234ENA.IRANMANESHTarbiatModares University,
IranM. A.HOSSEINZADEHTarbiatModares University,
IranI.GUTMANUniversity of Kragujevac, Kragujevac, SerbiaJournal Article20140429Todeschini et al. have recently suggested to consider multiplicative variants of additive graph invariants, which applied to the Zagreb indices would lead to the multiplicative Zagreb indices of a graph G, denoted by ( ) 1 G and ( ) 2 G , under the name first and second multiplicative Zagreb index, respectively. These are define as ( ) 2 1 ( ) ( ) v V G G G d v and ( ) ( ) ( ) ( ) 2 G d v d v G uv E G G , where dG(v) is the degree of the vertex v. In this paper we compute these indices for link and splice of graphs. In continuation, with use these graph operations, we compute the first and the second multiplicative Zagreb indices for a class of dendrimers.https://ijmc.kashanu.ac.ir/article_5234_5d78d182fd5f5510588695863d22ac27.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64893220120901Fourth Order and Fourth Sum Connectivity Indices of Tetrathiafulvalene Dendrimers155163523510.22052/ijmc.2012.5235ENR.HASNIUniversiti Malaysia
Terengganu, Terengganu, MalaysiaN. E.ARIFUniversiti Sains Malaysia,
MalaysiaJournal Article20140429The m-order connectivity index (G) m of a graph G is 1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i m d d d G where 1 2 1 ... i i im d d d runs over all paths of length m in G and i d denotes the degree of vertex i v . Also, 1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i ms d d d X G is its m-sum connectivity index. A dendrimer is an artificially manufactured or synthesized molecule built up from branched units called monomers. In this paper, the 4-order connectivity and 4-sum connectivity indices of tetrathiafulvalene dendrimers are computed.University of KashanIranian Journal of Mathematical Chemistry2228-64893220120901Wiener, Szeged and Vertex PI Indices of Regular Tessellations165183523610.22052/ijmc.2012.5236ENP.MANUELKuwait University, Safat, KuwaitI.RAJASINGHDepartment of Mathematics, Loyola College, Chennai 600 034, IndiaM.AROCKIARAJLoyola College, IndiaJournal Article20140429A lot of research and various techniques have been devoted for finding the topological descriptor Wiener index, but most of them deal with only particular cases. There exist three regular plane tessellations, composed of the same kind of regular polygons namely triangular, square, and hexagonal. Using edge congestion-sum problem, we devise a method to compute the Wiener index and demonstrate this method to all classes of regular tessellations. In addition, we obtain the vertex Szeged and vertex PI indices of regular tessellations.https://ijmc.kashanu.ac.ir/article_5236_78289d91e9c4adcf4e97d6b3d4df6ae0.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64893220120901A Zero One Programming Model for RNA Structures with Arclength ≥ 4185193523710.22052/ijmc.2012.5237ENG. H.SHIRDELUniversity of Qom, IranN.KAHKESHANIUniversity of Qom, IranJournal Article20140429In this paper, we consider RNA structures with arc-length 4 . First, we represent these structures as matrix models and zero-one linearprogramming problems. Then, we obtain an optimal solution for this problemusing an implicit enumeration method. The optimal solution corresponds toan RNA structure with the maximum number of hydrogen bonds.https://ijmc.kashanu.ac.ir/article_5237_2adcefe38fbcd3dcd45908fbab1bf628.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64893220120901Fourth-order Numerical Solution of a Fractional PDE with the Nonlinear Source Term in the Electroanalytical Chemistry195220514710.22052/ijmc.2012.5147ENM.ABBASZADEUniversity of Kashan, Kashan, I. R. IranM.MOHEBBIUniversity of Kashan, Kashan, I. R. IranJournal Article20120513The aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (PDE) in the electroanalytical chemistry. The space fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the Grunwald- Letnikov discretization of the Riemann-Liouville derivative to obtain a fully discrete implicit scheme and analyze the solvability, stability and convergence of proposed scheme using the Fourier method. The convergence order of method is O(t + n4). Numerical examples demonstrate the theoretical results and high accuracy of proposed scheme.https://ijmc.kashanu.ac.ir/article_5147_8f1fa0193ca2b5d2fa0695827d8270e9.pdf