2020-02-22T16:18:45Z
http://ijmc.kashanu.ac.ir/?_action=export&rf=summon&issue=862
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2012
3
2
On discriminativity of vertex-degree-based indices
I.
GUTMAN
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
2012
09
01
95
101
http://ijmc.kashanu.ac.ir/article_5224_29d7fc3b02b47874d7d11ce5fe2c7133.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2012
3
2
Computational and electrochemical studies on the redox reaction of 2-(2,3-dihydroxy phenyl)-1,3- dithiane in aqueous solution
M.
MAZLOUM-ARDAKANI
H.
BEITOLLAHI
H.
FARROKHPOUR
A.
KHOSHROO
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
2012
09
01
103
112
http://ijmc.kashanu.ac.ir/article_5227_86b1e26598de444a9b55282fa197f5d7.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2012
3
2
On the tutte polynomial of benzenoid chains
G.
FATH-TABAR
Z.
GHOLAM-REZAEI
A.
ASHRAFI
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
2012
09
01
113
119
http://ijmc.kashanu.ac.ir/article_5229_cec9488a7d94da91a18548f7209453da.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2012
3
2
Computing Wiener and hyper–Wiener indices of unitary Cayley graphs
A.
LOGHMAN
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
2012
09
01
121
125
http://ijmc.kashanu.ac.ir/article_5230_e9f9e2e5cb6d37900fb420cdfb2b8a61.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2012
3
2
Chromatic polynomials of some nanostars
S.
ALIKHANI
M.
IRANMANESH
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
2012
09
01
127
135
http://ijmc.kashanu.ac.ir/article_5232_f2deb6663cef65ba7ec4d809e55ff717.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2012
3
2
Note on multiple Zagreb indices
M.
GHORBANI
N.
AZIMI
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
2012
09
01
137
143
http://ijmc.kashanu.ac.ir/article_5233_17da40a7ce1e404c23e046541aa4eefb.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2012
3
2
On multiplicative Zagreb indices of graphs
A.
IRANMANESH
M.
HOSSEINZADEH
I.
GUTMAN
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
2012
09
01
145
154
http://ijmc.kashanu.ac.ir/article_5234_272192a88612b48b4a6b0b58729ae23e.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2012
3
2
Fourth order and fourth sum connectivity indices of tetrathiafulvalene dendrimers
R.
HASNI
N.
ARIF
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
2012
09
01
155
163
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2012
3
2
Wiener, Szeged and vertex PI indices of regular tessellations
P.
MANUEL
I.
RAJASINGH
M.
AROCKIARAJ
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
2012
09
01
165
183
http://ijmc.kashanu.ac.ir/article_5236_6f501380f518c50662d028c90adb0160.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2012
3
2
A zero one programming model for RNA structures with arclength ≥ 4
G.
SHIRDEL
N.
KAHKESHANI
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
2012
09
01
185
193
http://ijmc.kashanu.ac.ir/article_5237_aedc58958c2bbe2c635313b9aac5eed8.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2012
3
2
Fourth-order numerical solution of a fractional PDE with the nonlinear source term in the electroanalytical chemistry
M.
ABBASZADE
M.
MOHEBBI
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
2012
09
01
195
220
http://ijmc.kashanu.ac.ir/article_5147_55d4072ecb915e23ccc789254cf387c2.pdf