2012
3
2
2
0
On discriminativity of vertexdegreebased indices
2
2
A recently published paper [T. Došlić, this journal 3 (2012) 2534] considers the Zagreb indices of benzenoid systems, and points out their low discriminativity. We show that analogous results hold for a variety of vertexdegreebased 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.
1

95
101


I.
GUTMAN
University of Kragujevac, Kragujevac, Serbia
University of Kragujevac, Kragujevac, Serbia
I R Iran
Zagreb index
Vertexdegreebased indices
Benzenoid graph
Catacondensed benzenoid graph
Computational and electrochemical studies on the redox reaction of 2(2,3dihydroxy phenyl)1,3 dithiane in aqueous solution
2
2
Electrode potential of 2(2,3dihydroxy phenyl)1,3dithiane (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). DFTB3LYP calculations using 6311++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).
1

103
112


M.
MAZLOUMARDAKANI
Yazd University, I.R. Iran
Yazd University, I.R. Iran
I R Iran


H.
BEITOLLAHI
Yazd University, I.R. Iran
Yazd University, I.R. Iran
I R Iran


H.
FARROKHPOUR
Isfahan University of Technology, Iran
Isfahan University of Technology, Iran
I R Iran


A.
KHOSHROO
Isfahan University of Technology, Iran
Isfahan University of Technology, Iran
I R Iran
Redox reaction
Density functional theory
Computational chemistry
Cyclic voltammetry
On the tutte polynomial of benzenoid chains
2
2
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.
1

113
119


G.
FATHTABAR
University of Kashan,
I. R. Iran
University of Kashan,
I. R. Iran
I R Iran


Z.
GHOLAMREZAEI
University of Kashan,
I. R. Iran
University of Kashan,
I. R. Iran
I R Iran


A.
ASHRAFI
University of Kashan,
I. R. Iran
University of Kashan,
I. R. Iran
I R Iran
Benzenoid chain
Tutte polynomial
Graph
Computing Wiener and hyper–Wiener indices of unitary Cayley graphs
2
2
The unitary Cayley graph Xn has vertex set Zn = {0, 1,…, n1} 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.
1

121
125


A.
LOGHMAN
Payame Noor Universtiy, IRAN
Payame Noor Universtiy, IRAN
I R Iran
Unitary Cayley graphs
Wiener index
hyperWiener index
Chromatic polynomials of some nanostars
2
2
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.
1

127
135


S.
ALIKHANI
Yazd University, Iran
Yazd University, Iran
I R Iran


M.
IRANMANESH
Yazd University, Yazd, Iran
Yazd University, Yazd, Iran
I R Iran
Chromatic polynomial
Nanostar
Graph
Note on multiple Zagreb indices
2
2
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.
1

137
143


M.
GHORBANI
Shahid Rajaee Teacher Training
University, I. R. Iran
Shahid Rajaee Teacher Training
University,
I R Iran


N.
AZIMI
Shahid Rajaee Teacher Training
University, I. R. Iran;
Shahid Rajaee Teacher Training
University,
I R Iran
Zagreb indices
Vertex degree
Multiple Zagreb indices
On multiplicative Zagreb indices of graphs
2
2
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.
1

145
154


A.
IRANMANESH
TarbiatModares University,
Iran
TarbiatModares University,
Iran
I R Iran


M.
HOSSEINZADEH
TarbiatModares University,
Iran
TarbiatModares University,
Iran
I R Iran


I.
GUTMAN
University of Kragujevac, Kragujevac, Serbia
University of Kragujevac, Kragujevac, Serbia
I R Iran
Multiplicative Zagreb indices
Splice
Link
Chain graphs
Dendrimer
Fourth order and fourth sum connectivity indices of tetrathiafulvalene dendrimers
2
2
The morder 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 msum connectivity index. A dendrimer is an artificially manufactured or synthesized molecule built up from branched units called monomers. In this paper, the 4order connectivity and 4sum connectivity indices of tetrathiafulvalene dendrimers are computed.
1

155
163


R.
HASNI
Universiti Malaysia
Terengganu, Terengganu, Malaysia
Universiti Malaysia
Terengganu, Terengganu,
Malaysia


N.
ARIF
Universiti Sains Malaysia,
Malaysia
Universiti Sains Malaysia,
Malaysia
Malaysia
4Order connectivity index
4Sum connectivity index
Dendrimer
Graph
Wiener, Szeged and vertex PI indices of regular tessellations
2
2
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 congestionsum 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.
1

165
183


P.
MANUEL
Kuwait University, Safat, Kuwait
Kuwait University, Safat, Kuwait
Kuwait


I.
RAJASINGH
Department of Mathematics, Loyola College, Chennai 600 034, India
Department of Mathematics, Loyola College,
India


M.
AROCKIARAJ
Loyola College, India
Loyola College, India
India
Wiener index
Szeged index
PI index
Embedding
Congestion
Regular plane tessellations
A zero one programming model for RNA structures with arclength ≥ 4
2
2
In this paper, we consider RNA structures with arclength 4 . First, we represent these structures as matrix models and zeroone 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.
1

185
193


G.
SHIRDEL
University of Qom, Iran
University of Qom, Iran
I R Iran


N.
KAHKESHANI
University of Qom, Iran
University of Qom, Iran
I R Iran
RNA structure
Zeroone linear programming problem
Additive algorithm
Fourthorder numerical solution of a fractional PDE with the nonlinear source term in the electroanalytical chemistry
2
2
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 RiemannLiouville sense. In the proposed scheme we discretize the space derivative with a fourthorder compact scheme and use the Grunwald Letnikov discretization of the RiemannLiouville 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.
1

195
220


M.
ABBASZADE
University of Kashan, Kashan, I. R. Iran
University of Kashan, Kashan, I. R. Iran
I R Iran


M.
MOHEBBI
University of Kashan, Kashan, I. R. Iran
University of Kashan, Kashan, I. R. Iran
I R Iran
a_ mohebbi@kashanu.ac.ir
Electroanalytical chemistry
Reactionsubdiffusion
Compact finite difference
Fourier analysis
Solvability
Unconditional stability
Convergence