2015
6
2
2
0
Mpolynomial and degreebased topological indices
2
2
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 degreebased 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.
1

93
102


E.
Deutsch
Polytechnic Institute of New York University
Polytechnic Institute of New York University
USA
emericdeutsch@msn.com


S.
Klavžar
Faculty of Mathematics and Physics, University of Ljubljana, Slovenia
Faculty of Mathematics and Physics, University
Slovenia
sandi.klavzar@fmf.unilj.si
Degreebased topological index
Zagreb index
Randic index
Graph polynomial
Edgedecomposition of topological indices
2
2
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.
1

103
108


I.
Gutman
Faculty of Science, University of Kragujevac, Kragujevac, Serbia
Faculty of Science, University of Kragujevac,
Serbia
gutman@kg.ac.rs
Topological index
Molecular graph
edgedecomposition
coindex
Photoluminescence quantitative analysis of Gallic acid and Caffeine in green tea using multiway chemometric approaches
2
2
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 excitationemission data using chemometric approaches. Multiway 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
1

109
119


S.
Masoum
Department of Analytical Chemistry, Faculty of Chemistry, University of Kashan, Kashan, I.R. Iran
Department of Analytical Chemistry, Faculty
I R Iran
masoum@kashanu.ac.ir


S.
Heshmat
Department of Analytical Chemistry, Faculty of Chemistry, University of Kashan, Kashan, I.R. Iran
Department of Analytical Chemistry, Faculty
I R Iran
sh.heshmat@gmail.com
Green tea
Spectrofluorimetric analysis
Excitationemission data
Threeway chemometric methods
The maximal total irregularity of some connected graphs
2
2
The total irregularity of a graph G is defined as 〖irr〗_t (G)=1/2 ∑_(u,v∈V(G))▒〖d_ud_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.
1

121
128


M.
Eliasi
I R Iran
eliasi@math.iut.ac.ir
Total irregularity index
Gini index
Majorization
Trees
Unicyclic graphs
bicyclic graph
The reliability Wiener number of cartesian product graphs
2
2
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 wellknown 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.
1

129
135


D.
Rupnik Poklukar
University of Ljubljana
University of Ljubljana
Slovenia
darja.rupnik@fs.unilj.si


J.
Zerovnik
University of Ljubljana
University of Ljubljana
Slovenia
janez.zerovnik@fs.unilj.si
reliability
Wiener number
Wiener index
Cartesian product of graphs
A note on connectivity and lambdamodified Wiener index
2
2
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 edgeconnectivity. Our results also present the sufficient and necessary condition for reaching the lower bound.
1

137
143


W.
Gao
Yunnan normal university
Yunnan normal university
P. R. China
gaowei@ynnu.edu.cn


Y.
Gao
yunnan normal university
yunnan normal university
P. R. China
gaoyun@ynnu.edu.cn
Chemical graph theory
lambdamodified Wiener index
Connectivity
Edgeconnectivity
Trigonometrically fitted twostep obrechkoff methods for the numerical solution of periodic initial value problems
2
2
In this paper, we present a new twostep trigonometrically fitted symmetric Obrechkoff method. The method is based on the symmetric twostep Obrechkoff method, with eighth algebraic order, high phaselag 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.
1

145
161


A.
Shokri
Department of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran.
Department of Mathematics, Faculty of Basic
I R Iran
shokri2090@gmail.com


A.
Shokri
Department of Mathematics, Ahar Branch, Islamic Azad University, Ahar, Iran.
Department of Mathematics, Ahar Branch, Islamic
I R Iran
ashokri@iauahar.ac.ir


Sh.
Mostafavi
Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran.
Faculty of Mathematical Science, University
I R Iran
shabnammostafavi_91@yahoo.com


H.
Saadat
Department of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran
Department of Mathematics, Faculty of Basic
I R Iran
hosein67saadat@yahoo.com
Obrechkoff methods
Trigonometricallyfitting
Initial value problems
Symmetric multistep methods
Oscillating solution
Hypertubes of hypercubes
2
2
Hypertubes consisting of hypercubes of ndimensions were designed and formulas for substructures of vary dimensions established.
1

163
168


A.
ParvanMoldovan
BabesBolyai University, Cluj, Romania
BabesBolyai University, Cluj, Romania
Romania
eurosocmathchem@gmail.com


M.
Diudea
BabesBolyai University, Cluj, Romania
BabesBolyai University, Cluj, Romania
Romania
diudea@gmail.com
Graph
ncube
Hypertube
Hypertorus
ndimensional space
A nonstandard finite difference scheme for solving fractionalorder model of HIV1 infection of CD4^+ tcells
2
2
In this paper, we introduce fractionalorder into a model of HIV1 infection of CD4^+ Tcells. 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 fractionalorder HIV1 infection model. Numerical results show that the NSFD approach is easy to be implemented and accurated when applied to fractionalorder HIV1 infection model.
1

169
184


S.
Zibaei
Department of Mathematics, School of Mathematical Sciences, ValieAsr University of Rafsanjan, Rafsanjan, Iran
Department of Mathematics, School of Mathematical
I R Iran
s.zibaei@stu.vru.ac.ir


M.
Namjoo
Department of Mathematics, School of Mathematical Sciences, ValieAsr University of Rafsanjan, Rafsanjan, Iran
Department of Mathematics, School of Mathematical
I R Iran
namjoo@vru.ac.ir
HIV1 model
Nonstandard finite difference scheme
Fractional differential equations
GrunwaldLetnikov derivative
Stability
Open problems for equienergetic graphs
2
2
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, noncospectral trees, it is not known how to systematically construct any such pair. (2) If by numerical calculation one finds that two noncospectral graphs seem to be equienergetic, in the general case no method is known for proving that this indeed is the case.
1

185
187


I.
Gutman
Faculty of Science, University of Kragujevac, Kragujevac, Serbia
Faculty of Science, University of Kragujevac,
Serbia
gutman@kg.ac.rs
Graph energy
equienergetic graphs
Spectrum (of graph)