University of KashanIranian Journal of Mathematical Chemistry2228-64893Supplement 120121201Note on Properties of First Zagreb Index of Graphs15526910.22052/ijmc.2012.5269ENM.TAVAKOLIFerdowsi University of Mashhad, IranF.RAHBARNIAFerdowsi University of Mashhad, IranJournal Article20140504Let G be a graph. The first Zagreb M1(G) of graph G is defined as: M1(G) = uV(G) deg(u)2. In this paper, we prove that each even number except 4 and 8 is a first Zagreb index of a caterpillar. Also, we show that the fist Zagreb index cannot be an odd number. Moreover, we obtain the fist Zagreb index of some graph operations.University of KashanIranian Journal of Mathematical Chemistry2228-64893Supplement 120121201Eccentric Connectivity Index of Some Dendrimer Graphs718527010.22052/ijmc.2012.5270ENM.GHORBANIShahid Rajaee Teacher Training
University, I. R. Iran;KH.MALEKJANIShahid Rajaee Teacher Training
University, I. R. Iran;A.KHAKIShahid Rajaee Teacher Training
University, I. R. Iran;Journal Article20140504The eccentricity connectivity index of a molecular graph G is defined as (G) = aV(G) deg(a)ε(a), where ε(a) is defined as the length of a maximal path connecting a to other vertices of G and deg(a) is degree of vertex a. Here, we compute this topological index for some infinite classes of dendrimer graphs.University of KashanIranian Journal of Mathematical Chemistry2228-64893Supplement 120121201Computing GA4 Index of Some Graph Operations1928527110.22052/ijmc.2012.5271ENM.SAHELIUniversity of Kashan, I. R. IranM.JALALI RADUniversity of Kashan,
Kashan, I. R. IranJournal Article20140504The geometric-arithmetic index is another topological index was defined as 2 deg ( )deg ( ) ( ) deg ( ) deg ( ) G G uv E G G u v GA G u v , in which degree of vertex u denoted by degG (u). We now define a new version of GA index as 4 ( ) 2 ε ( )ε ( ) ( ) ε ( ) ε ( ) G G e uv E G G G u v GA G u v , where εG(u) is the eccentricity of vertex u. In this paper we compute this new topological index for two graph operations.University of KashanIranian Journal of Mathematical Chemistry2228-64893Supplement 120121201On Symmetry of Some Nano Structures2936527210.22052/ijmc.2012.5272ENM.GHORBANIShahid Rajaee Teacher Training
University, I. R. IranA.ZAEEMBASHIShahid Rajaee Teacher Training
University, I. R. IranM.SHAHREZAEIImam Hossein University,
I.R. IranA.TABATABAEI ADNANIIslamic Azad University, I. R. IranJournal Article20140504It is necessary to generate the automorphism group of a chemical graph in computer-aided structure elucidation. An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [dij], where for i≠j, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for distinct nuclei. A.T. Balaban introduced some monster graphs and then M. Randic computed complexity indices of them (see A.T. Balaban, Rev. Roum. Chim. 18(1973) 841-853 and M. Randic, Croat. Chem. Acta 74(3)(2001) 683- 705). In this paper, we describe a simple method, by means of which it is possible to calculate the automorphism group of weighted graphs.University of KashanIranian Journal of Mathematical Chemistry2228-64893Supplement 120121201Applications of Graph Operations3743527310.22052/ijmc.2012.5273ENM.TAVAKOLIFerdowsi University of Mashhad, IranF.RAHBARNIAFerdowsi University of Mashhad, IranJournal Article20140504In this paper, some applications of our earlier results in working with chemical graphs are presented.University of KashanIranian Journal of Mathematical Chemistry2228-64893Supplement 120121201Geometric-Arithmetic Index of Hamiltonian Fullerenes4550527410.22052/ijmc.2012.5274ENH. R.MOSTAFAEIIslamic Azad University, Tehran, IranA.ZAEEMBASHIShahid Rajaee Teacher Training
University, Tehran, I. R. IranM.OSTAD RAHIMITehran North Branch, Islamic Azad University,
IranJournal Article20140504A graph that contains a Hamiltonian cycle is called a Hamiltonian graph. In this paper we compute the first and the second geometric – arithmetic indices of Hamiltonian graphs. Then we apply our results to obtain some bounds for fullerene.University of KashanIranian Journal of Mathematical Chemistry2228-64893Supplement 120121201On Counting Polynomials of Some Nanostructures5158527510.22052/ijmc.2012.5275ENM.GHORBANIShahid Rajaee Teacher Training
University, I. R. IranM.SONGHORIShahid Rajaee Teacher Training
University, I. R. IranJournal Article20140504The Omega polynomial(x) was recently proposed by Diudea, based on the length of strips in given graph G. The Sadhana polynomial has been defined to evaluate the Sadhana index of a molecular graph. The PI polynomial is another molecular descriptor. In this paper we compute these three polynomials for some infinite classes of nanostructures.University of KashanIranian Journal of Mathematical Chemistry2228-64893Supplement 120121201Computing Chemical Properties of Molecules by Graphs and Rank Polynomials5965527610.22052/ijmc.2012.5276ENM.MOGHARRABPersian Gulf University,
I.R. IranG. H.FATH-TABARUniversity of
Kashan, I. R. IranJournal Article20140504The topological index of a graph G is a numeric quantity related to G which is invariant under automorphisms of G. The Tutte polynomial of is a polynomial in two variables defined for every undirected graph contains information about connectivity of the graph. The Padmakar-Ivan, vertex Padmakar-Ivan polynomials of a graph are polynomials in one variable defined for every simple connected graphs that are undirected. In this paper, we compute these polynomials of two infinite classes of dendrimer nanostars.University of KashanIranian Journal of Mathematical Chemistry2228-64893Supplement 120121201A Note on Atom Bond Connectivity Index6775527710.22052/ijmc.2012.5277ENS.HEIDARI RADShahid Rajaee Teacher Training
University, I. R. IranA.KHAKIShahid Rajaee Teacher Training
University, I. R. IranJournal Article20140504The atom bond connectivity index of a graph is a new topological index was defined by E. Estrada as ABC(G) uvE (dG(u) dG(v) 2) / dG(u)dG(v) , where G d ( u ) denotes degree of vertex u. In this paper we present some bounds of this new topological index.