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)= {xV(G) d(x,u) d(x,v)} and N2(e | G)= {xV(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