University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
3
2
2012
09
01
On discriminativity of vertex-degree-based indices
95
101
EN
I.
GUTMAN
University of Kragujevac, Kragujevac, Serbia
10.22052/ijmc.2012.5224
A 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.
Zagreb index,Vertex-degree-based indices,Benzenoid graph,Catacondensed benzenoid graph
http://ijmc.kashanu.ac.ir/article_5224.html
http://ijmc.kashanu.ac.ir/article_5224_29d7fc3b02b47874d7d11ce5fe2c7133.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
3
2
2012
09
01
Computational and electrochemical studies on the redox reaction of 2-(2,3-dihydroxy phenyl)-1,3- dithiane in aqueous solution
103
112
EN
M.
MAZLOUM-ARDAKANI
Yazd University, I.R. Iran
H.
BEITOLLAHI
Yazd University, I.R. Iran
H.
FARROKHPOUR
Isfahan University of Technology, Iran
A.
R.
KHOSHROO
Isfahan University of Technology, Iran
10.22052/ijmc.2012.5227
Electrode 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).
Redox reaction,Density functional theory,Computational chemistry,Cyclic voltammetry
http://ijmc.kashanu.ac.ir/article_5227.html
http://ijmc.kashanu.ac.ir/article_5227_86b1e26598de444a9b55282fa197f5d7.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
3
2
2012
09
01
On the tutte polynomial of benzenoid chains
113
119
EN
G.
FATH-TABAR
University of Kashan,
I. R. Iran
Z.
GHOLAM-REZAEI
University of Kashan,
I. R. Iran
A.
R.
ASHRAFI
University of Kashan,
I. R. Iran
10.22052/ijmc.2012.5229
The 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.
Benzenoid chain,Tutte polynomial,graph
http://ijmc.kashanu.ac.ir/article_5229.html
http://ijmc.kashanu.ac.ir/article_5229_cec9488a7d94da91a18548f7209453da.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
3
2
2012
09
01
Computing Wiener and hyper–Wiener indices of unitary Cayley graphs
121
125
EN
A.
LOGHMAN
Payame Noor Universtiy, IRAN
10.22052/ijmc.2012.5230
The 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.
Unitary Cayley graphs,Wiener index,hyper-Wiener index
http://ijmc.kashanu.ac.ir/article_5230.html
http://ijmc.kashanu.ac.ir/article_5230_e9f9e2e5cb6d37900fb420cdfb2b8a61.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
3
2
2012
09
01
Chromatic polynomials of some nanostars
127
135
EN
S.
ALIKHANI
Yazd University, Iran
M.
A.
IRANMANESH
Yazd University, Yazd, Iran
10.22052/ijmc.2012.5232
Let 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.
Chromatic polynomial,Nanostar,graph
http://ijmc.kashanu.ac.ir/article_5232.html
http://ijmc.kashanu.ac.ir/article_5232_f2deb6663cef65ba7ec4d809e55ff717.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
3
2
2012
09
01
Note on multiple Zagreb indices
137
143
EN
M.
GHORBANI
Shahid Rajaee Teacher Training
University, I. R. Iran
N.
AZIMI
Shahid Rajaee Teacher Training
University, I. R. Iran;
10.22052/ijmc.2012.5233
The 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.
Zagreb indices,Vertex degree,Multiple Zagreb indices
http://ijmc.kashanu.ac.ir/article_5233.html
http://ijmc.kashanu.ac.ir/article_5233_17da40a7ce1e404c23e046541aa4eefb.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
3
2
2012
09
01
On multiplicative Zagreb indices of graphs
145
154
EN
A.
IRANMANESH
TarbiatModares University,
Iran
M.
A.
HOSSEINZADEH
TarbiatModares University,
Iran
I.
GUTMAN
University of Kragujevac, Kragujevac, Serbia
10.22052/ijmc.2012.5234
Todeschini 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.
Multiplicative Zagreb indices,Splice,Link,Chain graphs,Dendrimer
http://ijmc.kashanu.ac.ir/article_5234.html
http://ijmc.kashanu.ac.ir/article_5234_272192a88612b48b4a6b0b58729ae23e.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
3
2
2012
09
01
Fourth order and fourth sum connectivity indices of tetrathiafulvalene dendrimers
155
163
EN
R.
HASNI
Universiti Malaysia
Terengganu, Terengganu, Malaysia
N.
E.
ARIF
Universiti Sains Malaysia,
Malaysia
10.22052/ijmc.2012.5235
The 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.
4-Order connectivity index,4-Sum connectivity index,Dendrimer,graph
http://ijmc.kashanu.ac.ir/article_5235.html
http://ijmc.kashanu.ac.ir/article_5235_d41d8cd98f00b204e9800998ecf8427e.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
3
2
2012
09
01
Wiener, Szeged and vertex PI indices of regular tessellations
165
183
EN
P.
MANUEL
Kuwait University, Safat, Kuwait
I.
RAJASINGH
Department of Mathematics, Loyola College, Chennai 600 034, India
M.
AROCKIARAJ
Loyola College, India
10.22052/ijmc.2012.5236
A 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.
Wiener index,Szeged index,PI index,Embedding,Congestion,Regular plane tessellations
http://ijmc.kashanu.ac.ir/article_5236.html
http://ijmc.kashanu.ac.ir/article_5236_6f501380f518c50662d028c90adb0160.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
3
2
2012
09
01
A zero one programming model for RNA structures with arclength ≥ 4
185
193
EN
G.
H.
SHIRDEL
University of Qom, Iran
N.
KAHKESHANI
University of Qom, Iran
10.22052/ijmc.2012.5237
In 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.
RNA structure,Zero-one linear programming problem,Additive algorithm
http://ijmc.kashanu.ac.ir/article_5237.html
http://ijmc.kashanu.ac.ir/article_5237_aedc58958c2bbe2c635313b9aac5eed8.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
3
2
2012
09
01
Fourth-order numerical solution of a fractional PDE with the nonlinear source term in the electroanalytical chemistry
195
220
EN
M.
ABBASZADE
University of Kashan, Kashan, I. R. Iran
M.
MOHEBBI
University of Kashan, Kashan, I. R. Iran
a_ mohebbi@kashanu.ac.ir
10.22052/ijmc.2012.5147
The 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.
Electroanalytical chemistry,Reaction-sub-diffusion,Compact finite difference,Fourier analysis,solvability,unconditional stability,convergence
http://ijmc.kashanu.ac.ir/article_5147.html
http://ijmc.kashanu.ac.ir/article_5147_55d4072ecb915e23ccc789254cf387c2.pdf