eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2012-09-01
3
2
95
101
10.22052/ijmc.2012.5224
5224
On discriminativity of vertex-degree-based indices
I. GUTMAN
1
University of Kragujevac, Kragujevac, Serbia
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.
http://ijmc.kashanu.ac.ir/article_5224_29d7fc3b02b47874d7d11ce5fe2c7133.pdf
Zagreb index
Vertex-degree-based indices
Benzenoid graph
Catacondensed benzenoid graph
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2012-09-01
3
2
103
112
10.22052/ijmc.2012.5227
5227
Computational and electrochemical studies on the redox reaction of 2-(2,3-dihydroxy phenyl)-1,3- dithiane in aqueous solution
M. MAZLOUM-ARDAKANI
1
H. BEITOLLAHI
2
H. FARROKHPOUR
3
A. KHOSHROO
4
Yazd University, I.R. Iran
Yazd University, I.R. Iran
Isfahan University of Technology, Iran
Isfahan University of Technology, Iran
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).
http://ijmc.kashanu.ac.ir/article_5227_86b1e26598de444a9b55282fa197f5d7.pdf
redox reaction
Density functional theory
Computational chemistry
Cyclic voltammetry
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2012-09-01
3
2
113
119
10.22052/ijmc.2012.5229
5229
On the tutte polynomial of benzenoid chains
G. FATH-TABAR
1
Z. GHOLAM-REZAEI
2
A. ASHRAFI
3
University of Kashan, I. R. Iran
University of Kashan, I. R. Iran
University of Kashan, I. R. Iran
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.
http://ijmc.kashanu.ac.ir/article_5229_cec9488a7d94da91a18548f7209453da.pdf
Benzenoid chain
Tutte polynomial
graph
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2012-09-01
3
2
121
125
10.22052/ijmc.2012.5230
5230
Computing Wiener and hyper–Wiener indices of unitary Cayley graphs
A. LOGHMAN
1
Payame Noor Universtiy, IRAN
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.
http://ijmc.kashanu.ac.ir/article_5230_e9f9e2e5cb6d37900fb420cdfb2b8a61.pdf
Unitary Cayley graphs
Wiener index
hyper-Wiener index
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2012-09-01
3
2
127
135
10.22052/ijmc.2012.5232
5232
Chromatic polynomials of some nanostars
S. ALIKHANI
1
M. IRANMANESH
2
Yazd University, Iran
Yazd University, Yazd, Iran
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.
http://ijmc.kashanu.ac.ir/article_5232_f2deb6663cef65ba7ec4d809e55ff717.pdf
Chromatic polynomial
Nanostar
graph
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2012-09-01
3
2
137
143
10.22052/ijmc.2012.5233
5233
Note on multiple Zagreb indices
M. GHORBANI
1
N. AZIMI
2
Shahid Rajaee Teacher Training University, I. R. Iran
Shahid Rajaee Teacher Training University, I. R. Iran;
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.
http://ijmc.kashanu.ac.ir/article_5233_17da40a7ce1e404c23e046541aa4eefb.pdf
Zagreb indices
Vertex degree
Multiple Zagreb indices
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2012-09-01
3
2
145
154
10.22052/ijmc.2012.5234
5234
On multiplicative Zagreb indices of graphs
A. IRANMANESH
1
M. HOSSEINZADEH
2
I. GUTMAN
3
TarbiatModares University, Iran
TarbiatModares University, Iran
University of Kragujevac, Kragujevac, Serbia
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.
http://ijmc.kashanu.ac.ir/article_5234_272192a88612b48b4a6b0b58729ae23e.pdf
Multiplicative Zagreb indices
Splice
Link
Chain graphs
Dendrimer
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2012-09-01
3
2
155
163
10.22052/ijmc.2012.5235
5235
Fourth order and fourth sum connectivity indices of tetrathiafulvalene dendrimers
R. HASNI
1
N. ARIF
2
Universiti Malaysia Terengganu, Terengganu, Malaysia
Universiti Sains Malaysia, Malaysia
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.
http://ijmc.kashanu.ac.ir/article_5235_d41d8cd98f00b204e9800998ecf8427e.pdf
4-Order connectivity index
4-Sum connectivity index
Dendrimer
graph
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2012-09-01
3
2
165
183
10.22052/ijmc.2012.5236
5236
Wiener, Szeged and vertex PI indices of regular tessellations
P. MANUEL
1
I. RAJASINGH
2
M. AROCKIARAJ
3
Kuwait University, Safat, Kuwait
Department of Mathematics, Loyola College, Chennai 600 034, India
Loyola College, India
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.
http://ijmc.kashanu.ac.ir/article_5236_6f501380f518c50662d028c90adb0160.pdf
Wiener index
Szeged index
PI index
Embedding
Congestion
Regular plane tessellations
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2012-09-01
3
2
185
193
10.22052/ijmc.2012.5237
5237
A zero one programming model for RNA structures with arclength ≥ 4
G. SHIRDEL
1
N. KAHKESHANI
2
University of Qom, Iran
University of Qom, Iran
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.
http://ijmc.kashanu.ac.ir/article_5237_aedc58958c2bbe2c635313b9aac5eed8.pdf
RNA structure
Zero-one linear programming problem
Additive algorithm
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2012-09-01
3
2
195
220
10.22052/ijmc.2012.5147
5147
Fourth-order numerical solution of a fractional PDE with the nonlinear source term in the electroanalytical chemistry
M. ABBASZADE
1
M. MOHEBBI
a_ mohebbi@kashanu.ac.ir
2
University of Kashan, Kashan, I. R. Iran
University of Kashan, Kashan, I. R. Iran
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.
http://ijmc.kashanu.ac.ir/article_5147_55d4072ecb915e23ccc789254cf387c2.pdf
Electroanalytical chemistry
Reaction-sub-diffusion
Compact finite difference
Fourier analysis
solvability
unconditional stability
Convergence