Iranian J. Math. Chem. University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 University of Kashan 70 10.22052/ijmc.2012.5197 Research Paper Chebyshev finite difference method for a two−point boundary value problems with applications to chemical reactor theory ChFD Method for Boundary Value Problems Saadatmandi A. University of Kashan Azizi M. R. Shariaty Technical College 01 02 2012 3 1 1 7 20 12 2011 26 01 2012 Copyright © 2012, University of Kashan. 2012 http://ijmc.kashanu.ac.ir/article_5197.html

In this paper, a Chebyshev finite difference method has been proposed in order to solve nonlinear two-point boundary value problems for second order nonlinear differential equations. A problem arising from chemical reactor theory is then considered. The approach consists of reducing the problem to a set of algebraic equations. This method can be regarded as a non-uniform finite difference scheme. The method is computationally attractive and applications are demonstrated through an illustrative example. Also a comparison is made with existing results.

Chemical reactor Chebyshev finite difference method Numerical methods Boundary value problems Gauss–Lobatto nodes
Iranian J. Math. Chem. University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 University of Kashan 70 10.22052/ijmc.2012.5198 Research Paper Study of fullerenes by their algebraic properties Study of fullerenes by their Algebraic Properties Ghorbani M. Shahid Rajaee Teacher Training University Heidari Rad S. Shahid Rajaee Teacher Training University 01 02 2012 3 1 9 24 10 12 2011 01 02 2012 Copyright © 2012, University of Kashan. 2012 http://ijmc.kashanu.ac.ir/article_5198.html

The eigenvalues of a graph is the root of its characteristic polynomial. A fullerene F is a 3- connected graphs with entirely 12 pentagonal faces and n/2 -10 hexagonal faces, where n is the number of vertices of F. In this paper we investigate the eigenvalues of a class of fullerene graphs.

Molecular Graph Adjacency matrix Eigenvalue Fullerene
1. I. Gutman, The energy of a graph, Ber. Math.Statist. Sekt. Forsch. Graz 103 (1978) 1– 2. I. Gutman, The Energy of a Graph: Old and New Results, Algebraic Combinatorics and Applications, SpringerVerlag, Berlin, 2001. 3. I. Gutman and O. E. Polansky, Mathematical Concepts in Organic Chemistry, SpringerVerlag, Berlin, 1986. 4. H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl and R. E. Smalley, C60: Buckminsterfullerene. Nature 318 (1985) 162–163. 5. H. W. Kroto, J. E. Fichier and D. E. Cox, The Fullerene, Pergamon Press, New York, 6. D. Cvetković, M. Doob and H. Sachs, Spectra of Graphs: Theory and Applications (Pure and Applied Mathematics), Academic Press, 1997. 7. S. L. Lee, Y. L. Luo, B. E. Sagan and Y.-N. Yeh, Eigenvectors and eigenvalues of some special graphs, IV multilevel circulants. Int. J. Quant. Chem. 41 (1992) 105 – 116.
Iranian J. Math. Chem. University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 University of Kashan 70 10.22052/ijmc.2012.5199 Research Paper On discriminativity of Zagreb indices On Discriminativity of Zagreb Indices Doslic T. University of Zagreb 01 02 2012 3 1 25 34 10 01 2012 24 01 2012 Copyright © 2012, University of Kashan. 2012 http://ijmc.kashanu.ac.ir/article_5199.html

Zagreb indices belong to better known and better researched topological indices. We investigate here their ability to discriminate among benzenoid graphs and arrive at some quite unexpected conclusions. Along the way we establish tight (and sometimes sharp) lower and upper bounds on various classes of benzenoids.

Zagreb index Benzenoid graph Catacondensed benzenoid
1. A. R. Ashrafi, T. Došlić, A. Hamzeh, The Zagreb coindices of graph operations, Discrete Appl. Math. 158 (2010) 1571–1578. 2. J. Braun, A. Kerber, M. Meringer, C. Rucker, Similarity of molecular descriptors: the equivalence of Zagreb indices and walk counts, MATCH Commun. Math. Comput. Chem. 54 (2005), 163–176. 3. D. de Caen, An upper bound on the sum of squares of degrees in a graph, Discrete Math. 185 (1998) 245–248. 4. S. J. Cyvin, I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Lec. Notes in Chemistry, Springer, Heidelberg, 1988. 5. K. Ch. Das, Maximizing the sum of the squares of the degrees of a graph, Discrete Math. 285 (2004) 57–66. 6. K. Ch. Das, I. Gutman, Some properties of the second Zagreb index, MATCH Commun. Math. Comput. Chem. 52 (2004) 103–112. 7. T. Došlić, Vertex-Weighted Wiener Polynomials for Composite Graphs, Ars Math. Contemp. 1 (2008) 66–80. 8. I. Gutman, K. Ch. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004) 83–92. 9. M. H. Khalifeh, H. Yousefi-Azari, A. R. Ashrafi, The first and second Zagreb indices of graph operations, Discrete Appl. Math. 157 (2009) 804–811. 10. M. H. Khalifeh, H. Yousefi-Azari, A. R. Ashrafi, S.Wagner, Some new results on distance-based graph invariants, Europ. J. Combin. 30 (2009) 1149–1163. 11. D. J. Klein, T. Došlić, D. Bonchev, Vertex-weightings for distance moments and thorny graphs, Discrete Appl. Math. 155 (2007) 2294–2302. 12. V. Nikiforov, The sum of the squares of degrees: an overdue assignment, arXiv:math/0608660. 13. S. Nikolić, G. Kovačević, A. Miličević, N. Trinajstić, The Zagreb Indices 30 Years After, Croat. Chem. Acta 76 (2003) 113–124. 14. D. B. West, Introduction to Graph Theory, Prentice Hall, Upper Saddle River, 15. S. Yamaguchi, Estimating the Zagreb indices and the spectral radius of triangle-and quadrangle-free connected graphs, Chem. Phys. Lett. 458 (2008) 396–398. 16. Y. S. Yoon, J. K. Kim, A relationship between bounds on the sum of squares of degrees of graph, J. Appl. Math. & Comput. 21 (2006) 233–238. 17. B. Zhou, I. Gutman, Relations between Wiener, hyper-Wiener and Zagreb indices, Chem. Phys. Lett. 394 (2004) 93–95. 18. B. Zhou, Upper bounds for the Zagreb indices and the spectral radius of seriesparallel graphs, Int. J. Quant. Chem. 107 (2007) 875–878. 19. B. Zhou, N. Trinajstić, On reciprocal molecular topological index, J. Math. Chem. 44 (2008) 235–243.
Iranian J. Math. Chem. University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 University of Kashan 70 10.22052/ijmc.2012.5200 Research Paper Centric connectivity index by shell matrices Centric connectivity index by shell matrices Diudea M. V. Babes-Bolyai University 01 02 2012 3 1 35 43 10 01 2012 10 02 2012 Copyright © 2012, University of Kashan. 2012 http://ijmc.kashanu.ac.ir/article_5200.html

Relative centricity RC values of vertices/atoms are calculated within the Distance Detour and Cluj-Distance criteria on their corresponding Shell transforms. The vertex RC distribution in a molecular graph gives atom equivalence classes, useful in interpretation of NMR spectra. Timed by vertex valences, RC provides a new index, called Centric Connectivity CC, which can be useful in the topological characterization of graphs and in QSAR/QSPR studies.

Graph theory Cluj matrix Relative centricity Centric connectivity index
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Iranian J. Math. Chem. University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 University of Kashan 70 10.22052/ijmc.2012.5201 Research Paper Distance-based topological indices of tensor product of graphs Distance-Based Topological Indices of Tensor Product of Graphs Nadjafi-Arani M. J. University of Kashan Khodashenas H. University of Kashan 01 02 2012 3 1 45 53 10 06 2011 31 12 2011 Copyright © 2012, University of Kashan. 2012 http://ijmc.kashanu.ac.ir/article_5201.html

Let G and H be connected graphs. The tensor product G + H is a graph with vertex set V(G+H) = V (G) X V(H) and edge set E(G + H) ={(a , b)(x , y)| ax ∈ E(G) & by ∈ E(H)}. The graph H is called the strongly triangular if for every vertex u and v there exists a vertex w adjacent to both of them. In this article the tensor product of G + H under some distancebased topological indices are investigated, when H is a strongly triangular graph. As a special case most of results given by Hoji, Luob and Vumara in [Wiener and vertex PI indices of Kronecker products of graphs, Discrete Appl. Math., 158 (2010), 1848-1855] will be deduced.

tensor product Wiener type invariant Strongly triangular graph
Iranian J. Math. Chem. University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 University of Kashan 70 10.22052/ijmc.2012.5209 Research Paper On the edge reverse Wiener indices of TUC4C8(S) nanotubes On the edge reverse Wiener indices of TUC4C8(S) nanotubes Mahmiani A. Payame Noor University Khormali O. Tarbiat Modares University Iranmanesh A. Tarbiat Modares University 01 02 2012 3 1 55 65 01 01 2012 09 02 2012 Copyright © 2012, University of Kashan. 2012 http://ijmc.kashanu.ac.ir/article_5209.html

The edge versions of reverse Wiener indices were introduced by Mahmiani et al. very recently. In this paper, we find their relation with ordinary (vertex) Wiener index in some graphs. Also, we compute them for trees and TUC4C8(s) naotubes.

Molecular Graph Molecular matrix Reveres Wiener indices Edge reverse Wiener indices Distance of graph line graph Nanotubes
Iranian J. Math. Chem. University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 University of Kashan 70 10.22052/ijmc.2012.5219 Research Paper Computing the Szeged index of 4,4 ׳-bipyridinium dendrimer ARJOMANFAR A. Shar-e-Ray Branch,Iran GHOLAMI N. Islamic Azad University, Izeh Branch, Khouzestan, Iran 01 02 2012 3 1 67 72 29 04 2014 29 04 2014 Copyright © 2012, University of Kashan. 2012 http://ijmc.kashanu.ac.ir/article_5219.html

Let e be an edge of a G connecting the vertices u and v. Define two sets N1 (e | G) and N2(e |G) as N1(e | G)= {xV(G) d(x,u) d(x,v)} and N2(e | G)= {xV(G) d(x,v) d(x,u) }.The number of elements of N1(e | G) and N2(e | G) are denoted by n1(e | G) and n2(e | G) , respectively. The Szeged index of the graph G is defined as Sz(G) ( ) ( ) 1 2 n e G n e G e E    . In this paper we compute the Szeged index of a 4,4 ׳-Bipyridinium dendrimer.

Molecular Graph Dendrimer Szeged index 4 4 ׳-Bipyridinium
Iranian J. Math. Chem. University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 University of Kashan 70 10.22052/ijmc.2012.5220 Research Paper Some topological indices of graphs and some inequalities MOGHARRAB M. Persian Gulf University, Bushehr, Iran KHEZRI–MOGHADDAM B. Payame Noor University, Shiraz, Iran 01 02 2012 3 1 73 80 29 04 2014 29 04 2014 Copyright © 2012, University of Kashan. 2012 http://ijmc.kashanu.ac.ir/article_5220.html

Let G be a graph. In this paper, we study the eccentric connectivity index, the new version of the second Zagreb index and the forth geometric–arithmetic index.. The basic properties of these novel graph descriptors and some inequalities for them are established.

topological index Eccentric connectivity Geometric–arithmetic Zagreb index Cauchy–Schwarz inequality
Iranian J. Math. Chem. University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 University of Kashan 70 10.22052/ijmc.2012.5221 Research Paper Automatic graph construction of periodic open tubulene ((5,6,7)3) and computation of its Wiener, PI, and Szeged indices YOOSOFAN A. University of Kashan, Iran NAMAZI−FARD M. University of Kashan, Iran 01 02 2012 3 1 81 94 29 04 2014 29 04 2014 Copyright © 2012, University of Kashan. 2012 http://ijmc.kashanu.ac.ir/article_5221.html

The mathematical properties of nano molecules are an interesting branch of nanoscience for researches nowadays. The periodic open single wall tubulene is one of the nano molecules which is built up from two caps and a distancing nanotube/neck. We discuss how to automatically construct the graph of this molecule and plot the graph by spring layout algorithm in graphviz and netwrokx packages. The similarity between the shape of this molecule and the plotted graph is a consequence of our work. Furthermore, the Wiener, Szeged and PI indices of this molecule are computed.

Open tubulene topological index Szeged index Wiener index PI index