University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 3 1 2012 02 01 Chebyshev finite difference method for a two−point boundary value problems with applications to chemical reactor theory 1 7 EN A. Saadatmandi University of Kashan saadatmandi@kashanu.ac.ir M. R. Azizi Shariaty Technical College 10.22052/ijmc.2012.5197 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 http://ijmc.kashanu.ac.ir/article_5197.html http://ijmc.kashanu.ac.ir/article_5197_e39896886e9c361a7e56fda0b7f221a5.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 3 1 2012 02 01 Study of fullerenes by their algebraic properties 9 24 EN M. Ghorbani Shahid Rajaee Teacher Training University ghorbani30@gmail.com S. Heidari Rad Shahid Rajaee Teacher Training University 10.22052/ijmc.2012.5198 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 http://ijmc.kashanu.ac.ir/article_5198.html http://ijmc.kashanu.ac.ir/article_5198_a8fa41f6fd14aa9bd445b3b2f8726e3b.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 3 1 2012 02 01 On discriminativity of Zagreb indices 25 34 EN T. Doslic University of Zagreb doslic@master.grad.hr 10.22052/ijmc.2012.5199 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 http://ijmc.kashanu.ac.ir/article_5199.html http://ijmc.kashanu.ac.ir/article_5199_c6ae7c7fcc36f66e8bee02e54e98d61a.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 3 1 2012 02 01 Centric connectivity index by shell matrices 35 43 EN M. V. Diudea Babes-Bolyai University diudea@gmail.com 10.22052/ijmc.2012.5200 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 http://ijmc.kashanu.ac.ir/article_5200.html http://ijmc.kashanu.ac.ir/article_5200_d41d8cd98f00b204e9800998ecf8427e.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 3 1 2012 02 01 Distance-based topological indices of tensor product of graphs 45 53 EN M. J. Nadjafi-Arani University of Kashan mjnajafiarani@gmail.com H. Khodashenas University of Kashan khodashenas@kashanu.ac.ir 10.22052/ijmc.2012.5201 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 http://ijmc.kashanu.ac.ir/article_5201.html http://ijmc.kashanu.ac.ir/article_5201_d41d8cd98f00b204e9800998ecf8427e.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 3 1 2012 02 01 On the edge reverse Wiener indices of TUC4C8(S) nanotubes 55 65 EN A. Mahmiani Payame Noor University O. Khormali Tarbiat Modares University A. Iranmanesh Tarbiat Modares University iranmanesh@modares.ac.i 10.22052/ijmc.2012.5209 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 http://ijmc.kashanu.ac.ir/article_5209.html http://ijmc.kashanu.ac.ir/article_5209_2f3c005d91db72be764cbb2f564ab33e.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 3 1 2012 02 01 Computing the Szeged index of 4,4 ׳-bipyridinium dendrimer 67 72 EN A. ARJOMANFAR Shar-e-Ray Branch,Iran N. GHOLAMI Islamic Azad University, Izeh Branch, Khouzestan, Iran 10.22052/ijmc.2012.5219 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 http://ijmc.kashanu.ac.ir/article_5219.html http://ijmc.kashanu.ac.ir/article_5219_15c1f93cb85459d4528af627573c4871.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 3 1 2012 02 01 Some topological indices of graphs and some inequalities 73 80 EN M. MOGHARRAB Persian Gulf University, Bushehr, Iran B. KHEZRI–MOGHADDAM Payame Noor University, Shiraz, Iran 10.22052/ijmc.2012.5220 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 http://ijmc.kashanu.ac.ir/article_5220.html http://ijmc.kashanu.ac.ir/article_5220_4344681665ed2139c3c285378453c9ad.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 3 1 2012 02 01 Automatic graph construction of periodic open tubulene ((5,6,7)3) and computation of its Wiener, PI, and Szeged indices 81 94 EN A. YOOSOFAN University of Kashan, Iran M. NAMAZI−FARD University of Kashan, Iran 10.22052/ijmc.2012.5221 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 http://ijmc.kashanu.ac.ir/article_5221.html http://ijmc.kashanu.ac.ir/article_5221_7e3ced6b5d005ed92da509c1085bd32a.pdf