University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
6
2
2015
10
01
M-polynomial and degree-based topological indices
93
102
EN
E.
Deutsch
Polytechnic Institute of New York University
emericdeutsch@msn.com
S.
Klavžar
Faculty of Mathematics and Physics, University of Ljubljana, Slovenia
sandi.klavzar@fmf.uni-lj.si
10.22052/ijmc.2015.10106
Let $G$ be a graph and let $m_{ij}(G)$, $i,jge 1$, be the number of edges $uv$ of $G$ such that ${d_v(G), d_u(G)} = {i,j}$. The {em $M$-polynomial} of $G$ is introduced with $displaystyle{M(G;x,y) = sum_{ile j} m_{ij}(G)x^iy^j}$. It is shown that degree-based topological indices can be routinely computed from the polynomial, thus reducing the problem of their determination in each particular case to the single problem of determining the $M$-polynomial. The new approach is also illustrated with examples.
Degree-based topological index,Zagreb index,Randic index,Graph polynomial
http://ijmc.kashanu.ac.ir/article_10106.html
http://ijmc.kashanu.ac.ir/article_10106_9757adf6f41e068e07ffdc82bc9d1b38.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
6
2
2015
10
01
Edge-decomposition of topological indices
103
108
EN
I.
Gutman
Faculty of Science, University of Kragujevac, Kragujevac, Serbia
gutman@kg.ac.rs
10.22052/ijmc.2015.10107
The topological indices, defined as the sum of contributions of all pairs of vertices (among which are the Wiener, Harary, hyper–Wiener indices, degree distance, and many others), are expressed in terms of contributions of edges and pairs of edges.
topological index,Molecular Graph,edge-decomposition,coindex
http://ijmc.kashanu.ac.ir/article_10107.html
http://ijmc.kashanu.ac.ir/article_10107_7219f11930f0bb2a7a243517ae34b7d6.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
6
2
2015
10
01
Photoluminescence quantitative analysis of Gallic acid and Caffeine in green tea using multi-way chemometric approaches
109
119
EN
S.
Masoum
Department of Analytical Chemistry, Faculty of Chemistry, University of Kashan, Kashan, I.R. Iran
masoum@kashanu.ac.ir
S.
Heshmat
Department of Analytical Chemistry, Faculty of Chemistry, University of Kashan, Kashan, I.R. Iran
sh.heshmat@gmail.com
10.22052/ijmc.2015.10410
Green tea is considered as a dietary source of antioxidant nutrients, which acts upon human health. Green tea leaves contain three main components in the form of simple hydroxy benzoic acids such as gallic acid, propyl gallate and xanthic bases (caffeine), have been reported to prevent or delay a number of degenerative diseases and act mainly upon the central nervous system and stimulating wakefulness. Therefore, it is important to establish a simple and reliable analytical method for determination of these compounds in the presence of unexpected interferences in the green tea sample. In this research, a rapid and sensitive method was used for the direct determination of gallic acid and caffeine in green tea that is based on excitation-emission data using chemometric approaches. Multi-way chemometric models can be used to study such data, providing estimates of the spectra and concentration profiles of the underlying chemical analytes. A high percentage of recoveries for the spiked green tea for gallic acid (i.e. 96.15 %-109.78 %) and caffeine (i.e. 93.75% -101.57%) indicate the high accuracies of the proposed calibration methods for the assessment of gallic acid and caffeine in green tea
Green tea,Spectrofluorimetric analysis,Excitation-emission data,Three-way chemometric methods
http://ijmc.kashanu.ac.ir/article_10410.html
http://ijmc.kashanu.ac.ir/article_10410_93e154715e1cdd857466860b3bf7ca62.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
6
2
2015
10
01
The maximal total irregularity of some connected graphs
121
128
EN
M.
Eliasi
eliasi@math.iut.ac.ir
10.22052/ijmc.2015.10427
The total irregularity of a graph G is defined as 〖irr〗_t (G)=1/2 ∑_(u,v∈V(G))▒〖|d_u-d_v |〗, where d_u denotes the degree of a vertex u∈V(G). In this paper by using the Gini index, we obtain the ordering of the total irregularity index for some classes of connected graphs, with the same number of vertices.
Total irregularity index,Gini index,majorization,Trees,Unicyclic graphs,bicyclic graph
http://ijmc.kashanu.ac.ir/article_10427.html
http://ijmc.kashanu.ac.ir/article_10427_9fae099b55610cd9a9d16305077bd5a4.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
6
2
2015
10
01
The reliability Wiener number of cartesian product graphs
129
135
EN
D.
Rupnik Poklukar
University of Ljubljana
darja.rupnik@fs.uni-lj.si
J.
Zerovnik
University of Ljubljana
janez.zerovnik@fs.uni-lj.si
10.22052/ijmc.2015.10428
Reliability Wiener number is a modification of the original Wiener number in which probabilities are assigned to edges yielding a natural model in which there are some (or all) bonds in the molecule that are not static. Various probabilities naturally allow modelling different types of chemical bonds because chemical bonds are of different types and it is well-known that under certain conditions the bonds can break with certain probability. This is fully taken into account in quantum chemistry. In the model considered here, probabilistic nature is taken into account and at the same time the conceptual simplicity of the discrete graph theoretical model is preserved. Here we extend previous studies by deriving a formula for the reliability Wiener number of a Cartesian product of graphs.
Reliability,Wiener number,Wiener index,Cartesian product of graphs
http://ijmc.kashanu.ac.ir/article_10428.html
http://ijmc.kashanu.ac.ir/article_10428_07180c1016b1b2b03841010eac54b78f.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
6
2
2015
10
01
A note on connectivity and lambda-modified Wiener index
137
143
EN
W.
Gao
Yunnan normal university
gaowei@ynnu.edu.cn
Y.
Gao
yunnan normal university
gaoyun@ynnu.edu.cn
10.22052/ijmc.2015.10429
In theoretical chemistry, -modified Wiener index is a graph invariant topological index to analyze the chemical properties of molecular structure. In this note, we determine the minimum -modified Wiener index of graph with fixed connectivity or edge-connectivity. Our results also present the sufficient and necessary condition for reaching the lower bound.
Chemical graph theory,lambda-modified Wiener index,connectivity,Edge-connectivity
http://ijmc.kashanu.ac.ir/article_10429.html
http://ijmc.kashanu.ac.ir/article_10429_01579a1608e80d4c9c5ad2257762be5e.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
6
2
2015
10
01
Trigonometrically fitted two-step obrechkoff methods for the numerical solution of periodic initial value problems
145
161
EN
A.
Shokri
Department of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran.
shokri2090@gmail.com
A.
A.
Shokri
Department of Mathematics, Ahar Branch, Islamic Azad University, Ahar, Iran.
a-shokri@iau-ahar.ac.ir
Sh.
Mostafavi
Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran.
shabnammostafavi_91@yahoo.com
H.
Saadat
Department of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran
hosein67saadat@yahoo.com
10.22052/ijmc.2015.10451
In this paper, we present a new two-step trigonometrically fitted symmetric Obrechkoff method. The method is based on the symmetric two-step Obrechkoff method, with eighth algebraic order, high phase-lag order and is constructed to solve IVPs with periodic solutions such as orbital problems. We compare the new method to some recently constructed optimized methods from the literature. The numerical results obtained by the new method for some problems show its superiority in efficiency, accuracy and stability.
Obrechkoff methods,Trigonometrically-fitting,Initial value problems,Symmetric multistep methods,Oscillating solution
http://ijmc.kashanu.ac.ir/article_10451.html
http://ijmc.kashanu.ac.ir/article_10451_e37900e24a74b6f240f6b1f76209f4e0.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
6
2
2015
10
01
Hyper-tubes of hyper-cubes
163
168
EN
A.
Parvan-Moldovan
Babes-Bolyai University, Cluj, Romania
eurosocmathchem@gmail.com
M.
V.
Diudea
Babes-Bolyai University, Cluj, Romania
diudea@gmail.com
10.22052/ijmc.2015.10479
Hyper-tubes consisting of hyper-cubes of n-dimensions were designed and formulas for substructures of vary dimensions established.
graph,n-cube,Hyper-tube,Hyper-torus,n-dimensional space
http://ijmc.kashanu.ac.ir/article_10479.html
http://ijmc.kashanu.ac.ir/article_10479_0a521af99de82678ff6a280a224f54a7.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
6
2
2015
10
01
A nonstandard finite difference scheme for solving fractional-order model of HIV-1 infection of CD4^{+} t-cells
169
184
EN
S.
Zibaei
Department of Mathematics, School of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
s.zibaei@stu.vru.ac.ir
M.
Namjoo
Department of Mathematics, School of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
namjoo@vru.ac.ir
10.22052/ijmc.2015.10843
In this paper, we introduce fractional-order into a model of HIV-1 infection of CD4^+ T--cells. We study the effect of the changing the average number of viral particles $N$ with different sets of initial conditions on the dynamics of the presented model. The nonstandard finite difference (NSFD) scheme is implemented to study the dynamic behaviors in the fractional--order HIV-1 infection model. Numerical results show that the NSFD approach is easy to be implemented and accurated when applied to fractional-order HIV-1 infection model.
HIV-1 model,Nonstandard finite difference scheme,Fractional differential equations,Grunwald-Letnikov derivative,Stability
http://ijmc.kashanu.ac.ir/article_10843.html
http://ijmc.kashanu.ac.ir/article_10843_596181178c783132f395514fe2e6bb51.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
6
2
2015
10
01
Open problems for equienergetic graphs
185
187
EN
I.
Gutman
Faculty of Science, University of Kragujevac, Kragujevac, Serbia
gutman@kg.ac.rs
10.22052/ijmc.2015.10844
The energy of a graph is equal to the sum of the absolute values of its eigenvalues. Two graphs of the same order are said to be equienergetic if their energies are equal. We point out the following two open problems for equienergetic graphs. (1) Although it is known that there are numerous pairs of equienergetic, non-cospectral trees, it is not known how to systematically construct any such pair. (2) If by numerical calculation one finds that two non-cospectral graphs seem to be equienergetic, in the general case no method is known for proving that this indeed is the case.
Graph energy,equienergetic graphs,Spectrum (of graph)
http://ijmc.kashanu.ac.ir/article_10844.html
http://ijmc.kashanu.ac.ir/article_10844_d32b4f131b209f2425a4517b4c86a2cb.pdf