On discriminativity of vertex-degree-based indices
I.
GUTMAN
University of Kragujevac, Kragujevac, Serbia
author
text
article
2012
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
3
v.
2
no.
2012
95
101
https://ijmc.kashanu.ac.ir/article_5224_29d7fc3b02b47874d7d11ce5fe2c7133.pdf
dx.doi.org/10.22052/ijmc.2012.5224
Computational and electrochemical studies on the redox reaction of 2-(2,3-dihydroxy phenyl)-1,3- dithiane in aqueous solution
M.
MAZLOUM-ARDAKANI
Yazd University, I.R. Iran
author
H.
BEITOLLAHI
Yazd University, I.R. Iran
author
H.
FARROKHPOUR
Isfahan University of Technology, Iran
author
A.
KHOSHROO
Isfahan University of Technology, Iran
author
text
article
2012
eng
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).
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
3
v.
2
no.
2012
103
112
https://ijmc.kashanu.ac.ir/article_5227_86b1e26598de444a9b55282fa197f5d7.pdf
dx.doi.org/10.22052/ijmc.2012.5227
On the tutte polynomial of benzenoid chains
G.
FATH-TABAR
University of Kashan,
I. R. Iran
author
Z.
GHOLAM-REZAEI
University of Kashan,
I. R. Iran
author
A.
ASHRAFI
University of Kashan,
I. R. Iran
author
text
article
2012
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
3
v.
2
no.
2012
113
119
https://ijmc.kashanu.ac.ir/article_5229_cec9488a7d94da91a18548f7209453da.pdf
dx.doi.org/10.22052/ijmc.2012.5229
Computing Wiener and hyper–Wiener indices of unitary Cayley graphs
A.
LOGHMAN
Payame Noor Universtiy, IRAN
author
text
article
2012
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
3
v.
2
no.
2012
121
125
https://ijmc.kashanu.ac.ir/article_5230_e9f9e2e5cb6d37900fb420cdfb2b8a61.pdf
dx.doi.org/10.22052/ijmc.2012.5230
Chromatic polynomials of some nanostars
S.
ALIKHANI
Yazd University, Iran
author
M.
IRANMANESH
Yazd University, Yazd, Iran
author
text
article
2012
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
3
v.
2
no.
2012
127
135
https://ijmc.kashanu.ac.ir/article_5232_f2deb6663cef65ba7ec4d809e55ff717.pdf
dx.doi.org/10.22052/ijmc.2012.5232
Note on multiple Zagreb indices
M.
GHORBANI
Shahid Rajaee Teacher Training
University, I. R. Iran
author
N.
AZIMI
Shahid Rajaee Teacher Training
University, I. R. Iran;
author
text
article
2012
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
3
v.
2
no.
2012
137
143
https://ijmc.kashanu.ac.ir/article_5233_17da40a7ce1e404c23e046541aa4eefb.pdf
dx.doi.org/10.22052/ijmc.2012.5233
On multiplicative Zagreb indices of graphs
A.
IRANMANESH
TarbiatModares University,
Iran
author
M.
HOSSEINZADEH
TarbiatModares University,
Iran
author
I.
GUTMAN
University of Kragujevac, Kragujevac, Serbia
author
text
article
2012
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
3
v.
2
no.
2012
145
154
https://ijmc.kashanu.ac.ir/article_5234_272192a88612b48b4a6b0b58729ae23e.pdf
dx.doi.org/10.22052/ijmc.2012.5234
Fourth order and fourth sum connectivity indices of tetrathiafulvalene dendrimers
R.
HASNI
Universiti Malaysia
Terengganu, Terengganu, Malaysia
author
N.
ARIF
Universiti Sains Malaysia,
Malaysia
author
text
article
2012
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
3
v.
2
no.
2012
155
163
https://ijmc.kashanu.ac.ir/article_5235_d41d8cd98f00b204e9800998ecf8427e.pdf
dx.doi.org/10.22052/ijmc.2012.5235
Wiener, Szeged and vertex PI indices of regular tessellations
P.
MANUEL
Kuwait University, Safat, Kuwait
author
I.
RAJASINGH
Department of Mathematics, Loyola College, Chennai 600 034, India
author
M.
AROCKIARAJ
Loyola College, India
author
text
article
2012
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
3
v.
2
no.
2012
165
183
https://ijmc.kashanu.ac.ir/article_5236_6f501380f518c50662d028c90adb0160.pdf
dx.doi.org/10.22052/ijmc.2012.5236
A zero one programming model for RNA structures with arclength ≥ 4
G.
SHIRDEL
University of Qom, Iran
author
N.
KAHKESHANI
University of Qom, Iran
author
text
article
2012
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
3
v.
2
no.
2012
185
193
https://ijmc.kashanu.ac.ir/article_5237_aedc58958c2bbe2c635313b9aac5eed8.pdf
dx.doi.org/10.22052/ijmc.2012.5237
Fourth-order numerical solution of a fractional PDE with the nonlinear source term in the electroanalytical chemistry
M.
ABBASZADE
University of Kashan, Kashan, I. R. Iran
author
M.
MOHEBBI
University of Kashan, Kashan, I. R. Iran
author
text
article
2012
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
3
v.
2
no.
2012
195
220
https://ijmc.kashanu.ac.ir/article_5147_55d4072ecb915e23ccc789254cf387c2.pdf
dx.doi.org/10.22052/ijmc.2012.5147