eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2015-10-01
6
2
93
102
10.22052/ijmc.2015.10106
10106
M-polynomial and degree-based topological indices
E. Deutsch
emericdeutsch@msn.com
1
S. Klavžar
sandi.klavzar@fmf.uni-lj.si
2
Polytechnic Institute of New York University
Faculty of Mathematics and Physics, University of Ljubljana, Slovenia
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.
http://ijmc.kashanu.ac.ir/article_10106_9757adf6f41e068e07ffdc82bc9d1b38.pdf
Degree-based topological index
Zagreb index
Randic index
Graph polynomial
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2015-10-01
6
2
103
108
10.22052/ijmc.2015.10107
10107
Edge-decomposition of topological indices
I. Gutman
gutman@kg.ac.rs
1
Faculty of Science, University of Kragujevac, Kragujevac, Serbia
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.
http://ijmc.kashanu.ac.ir/article_10107_7219f11930f0bb2a7a243517ae34b7d6.pdf
topological index
Molecular Graph
edge-decomposition
coindex
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2015-10-01
6
2
109
119
10.22052/ijmc.2015.10410
10410
Photoluminescence quantitative analysis of Gallic acid and Caffeine in green tea using multi-way chemometric approaches
S. Masoum
masoum@kashanu.ac.ir
1
S. Heshmat
sh.heshmat@gmail.com
2
Department of Analytical Chemistry, Faculty of Chemistry, University of Kashan, Kashan, I.R. Iran
Department of Analytical Chemistry, Faculty of Chemistry, University of Kashan, Kashan, I.R. Iran
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
http://ijmc.kashanu.ac.ir/article_10410_93e154715e1cdd857466860b3bf7ca62.pdf
Green tea
Spectrofluorimetric analysis
Excitation-emission data
Three-way chemometric methods
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2015-10-01
6
2
121
128
10.22052/ijmc.2015.10427
10427
The maximal total irregularity of some connected graphs
M. Eliasi
eliasi@math.iut.ac.ir
1
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.
http://ijmc.kashanu.ac.ir/article_10427_9fae099b55610cd9a9d16305077bd5a4.pdf
Total irregularity index
Gini index
majorization
Trees
Unicyclic graphs
bicyclic graph
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2015-10-01
6
2
129
135
10.22052/ijmc.2015.10428
10428
The reliability Wiener number of cartesian product graphs
D. Rupnik Poklukar
darja.rupnik@fs.uni-lj.si
1
J. Zerovnik
janez.zerovnik@fs.uni-lj.si
2
University of Ljubljana
University of Ljubljana
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.
http://ijmc.kashanu.ac.ir/article_10428_07180c1016b1b2b03841010eac54b78f.pdf
Reliability
Wiener number
Wiener index
Cartesian product of graphs
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2015-10-01
6
2
137
143
10.22052/ijmc.2015.10429
10429
A note on connectivity and lambda-modified Wiener index
W. Gao
gaowei@ynnu.edu.cn
1
Y. Gao
gaoyun@ynnu.edu.cn
2
Yunnan normal university
yunnan normal university
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.
http://ijmc.kashanu.ac.ir/article_10429_01579a1608e80d4c9c5ad2257762be5e.pdf
Chemical graph theory
lambda-modified Wiener index
connectivity
Edge-connectivity
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2015-10-01
6
2
145
161
10.22052/ijmc.2015.10451
10451
Trigonometrically fitted two-step obrechkoff methods for the numerical solution of periodic initial value problems
A. Shokri
shokri2090@gmail.com
1
A. Shokri
a-shokri@iau-ahar.ac.ir
2
Sh. Mostafavi
shabnammostafavi_91@yahoo.com
3
H. Saadat
hosein67saadat@yahoo.com
4
Department of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran.
Department of Mathematics, Ahar Branch, Islamic Azad University, Ahar, Iran.
Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran.
Department of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran
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.
http://ijmc.kashanu.ac.ir/article_10451_e37900e24a74b6f240f6b1f76209f4e0.pdf
Obrechkoff methods
Trigonometrically-fitting
Initial value problems
Symmetric multistep methods
Oscillating solution
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2015-10-01
6
2
163
168
10.22052/ijmc.2015.10479
10479
Hyper-tubes of hyper-cubes
A. Parvan-Moldovan
eurosocmathchem@gmail.com
1
M. Diudea
diudea@gmail.com
2
Babes-Bolyai University, Cluj, Romania
Babes-Bolyai University, Cluj, Romania
Hyper-tubes consisting of hyper-cubes of n-dimensions were designed and formulas for substructures of vary dimensions established.
http://ijmc.kashanu.ac.ir/article_10479_0a521af99de82678ff6a280a224f54a7.pdf
Graph
n-cube
Hyper-tube
Hyper-torus
n-dimensional space
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2015-10-01
6
2
169
184
10.22052/ijmc.2015.10843
10843
A nonstandard finite difference scheme for solving fractional-order model of HIV-1 infection of CD4^{+} t-cells
S. Zibaei
s.zibaei@stu.vru.ac.ir
1
M. Namjoo
namjoo@vru.ac.ir
2
Department of Mathematics, School of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
Department of Mathematics, School of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
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.
http://ijmc.kashanu.ac.ir/article_10843_596181178c783132f395514fe2e6bb51.pdf
HIV-1 model
Nonstandard finite difference scheme
Fractional differential equations
Grunwald-Letnikov derivative
Stability
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2015-10-01
6
2
185
187
10.22052/ijmc.2015.10844
10844
Open problems for equienergetic graphs
I. Gutman
gutman@kg.ac.rs
1
Faculty of Science, University of Kragujevac, Kragujevac, Serbia
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.
http://ijmc.kashanu.ac.ir/article_10844_d32b4f131b209f2425a4517b4c86a2cb.pdf
Graph energy
equienergetic graphs
Spectrum (of graph)