2016
7
1
1
110
Degree distance index of the Mycielskian and its complement
2
2
In this paper, we determine the degree distance of the complement of arbitrary Mycielskian graphs. It is well known that almost all graphs have diameter two. We determine this graphical invariant for the Mycielskian of graphs with diameter two.
1

1
9


A.
Behtoei
Imam Khomeini International University
Imam Khomeini International University
I R Iran
a.behtoei@sci.ikiu.ac.ir


M.
Anbarloei
Imam Khomeini International University
Imam Khomeini International University
I R Iran
m.anbarloei@sci.ikiu.ac.ir
Degree distance
Zagreb indices
Mycielskian
A note on vertexedge Wiener indices of graphs
2
2
The vertexedge Wiener index of a simple connected graph G is defined as the sum of distances between vertices and edges of G. Two possible distances D_1(u,eG) and D_2(u,eG) between a vertex u and an edge e of G were considered in the literature and according to them, the corresponding vertexedge Wiener indices W_{ve_1}(G) and W_{ve_2}(G) were introduced. In this paper, we present exact formulas for computing the vertexedge Wiener indices of two composite graphs named splice and link.
1

11
17


M.
Azari
Kazerun Branch, Islamic Azad University
Kazerun Branch, Islamic Azad University
I R Iran
mahdie.azari@gmail.com
Distance in graph
Vertexedge Wiener index
Splice
Link
Electrospunorganic nanofibers elaboration process investigations using BPs operational matrices
2
2
In this paper operational matrix of Bernstein Polynomials (BPs) is used to solve Bratu equation. This nonlinear equation appears in the particular elecotrospun nanofibers fabrication process framework. Elecotrospun organic nanofibers have been used for a large variety of filtration applications such as in nonwoven and filtration industries. By using operational matrix of fractional integration and multiplication the investigated equations are turned into set of algebraic equations. Numerical solutions show both accuracy and simplicity of the suggested approach.
1

19
27


H.
Jafari
University of Mazandaran
University of Mazandaran
I R Iran
jafari@umz.ac.ir


H.
Tajadodi
University of Sistan and Baluchestan
University of Sistan and Baluchestan
I R Iran
tajadodi@umz.ac.ir
Bratu equation
Elecotrospun nanofibers
Bernstein polynomials
operational matrix
Hosoya polynomials of random benzenoid chains
2
2
Let $G$ be a molecular graph with vertex set $V(G)$, $d_G(u, v)$ the topological distance between vertices $u$ and $v$ in $G$. The Hosoya polynomial $H(G, x)$ of $G$ is a polynomial $sumlimits_{{u, v}subseteq V(G)}x^{d_G(u, v)}$ in variable $x$. In this paper, we obtain an explicit analytical expression for the expected value of the Hosoya polynomial of a random benzenoid chain with $n$ hexagons. Furthermore, as corollaries, the expected values of the wellknown topological indices: Wiener index, hyperWiener index and TratchStankevitchZefirov index of a random benzenoid chain with $n$ hexagons can be obtained by simple mathematical calculations, which generates the results given by I. Gutman et al. [Wiener numbers of random benzenoid chains, Chem. Phys. Lett. 173 (1990) 403408].
1

29
38


S.J.
Xu
Lanzhou University
Lanzhou University
P. R. China
shjxu@lzu.edu.cn


Q.H.
He
Lanzhou University
Lanzhou University
P. R. China
heqh12@lzu.edu.cn


S.
Zhou
Jiangsu Normal University
Jiangsu Normal University
P. R. China
zhous@lzu.edu.cn


W.
Chan
waihchan@ied.edu.hk
waihchan@ied.edu.hk
P. R. China
waihchan@ied.edu.hk
Wiener index
Random benzenoid chain
Hosoya polynomial
Expected value
Generating function
Complete forcing numbers of polyphenyl systems
2
2
The idea of “forcing” has long been used in many research fields, such as colorings, orientations, geodetics and dominating sets in graph theory, as well as Latin squares, block designs and Steiner systems in combinatorics (see [1] and the references therein). Recently, the forcing on perfect matchings has been attracting more researchers attention. A forcing set of M is a subset of M contained in no other perfect matchings of G. A global forcing set of G, introduced by Vukiˇcevi´c et al., is a subset of E(G) on which there are distinct restrictions of any two different perfect matchings of G. Combining the above “forcing” and “global” ideas, Xu et al. [5] introduce and define a complete forcing set of G as a subset of E(G) on which the restriction of any perfect matching M of G is a forcing set of M. The minimum cardinality of complete forcing sets is the complete forcing number of G. In this paper, we give the explicit expressions for the complete forcing number of several classes of polyphenyl systems.
1

39
46


B.
Liu
School of Mathematical Sciences, Xinjiang Normal University,
Urumqi, Xinjiang 830054, P. R. China
School of Mathematical Sciences, Xinjiang
P. R. China
446297409@qq.com


H.
Bian
Department of Mathematics, Xinjiang Normal University,
Urumqi, Xinjiang 830054, P.R.China
Department of Mathematics, Xinjiang Normal
P. R. China
bh_1218@sina.com


H.
Yu
College of Mathematics and System Sciences, Xinjiang University,
Urumqi 830046, P.R.China
College of Mathematics and System Sciences,
P. R. China
yhz0611@163.com
Complete forcing number
Polyphenly system
Global forcing number
Quantitative structure activity relationship study of inhibitory activities of 5lipoxygenase and design new compounds by different chemometrics methods
2
2
A quantitative structureactivity relationship (QSAR) study was conducted for the prediction of inhibitory activity of 1phenyl[2H]tetrahydrotriazine3one analogues as inhibitors of 5Lipoxygenase. The inhibitory activities of the 1phenyl[2H]tetrahydrotriazine3one analogues modeled as a function of molecular structures using chemometrics methods such as multiple linear regression (MLR) and least squares support vector machines (LSSVM). The obtained models were applied to predict the inhibitory activity of compounds which were not in the modeling procedure. The results of models showed high prediction ability with root mean square error of prediction of 0.167 and 0.061 for MLR and LSSVM, respectively. The LSSVM method was used for prediction of inhibitory activity of the new inhibitor derivatives.
1

47
59


F.
BaghebanShahri
Chemistry,Arak Branch, Islamic Azad University
Chemistry,Arak Branch, Islamic Azad University
I R Iran
f.baghebanshahri@gmail.com


A.
Niazi
Chemistry,Arak Branch, Islamic Azad University
Chemistry,Arak Branch, Islamic Azad University
I R Iran
chemistrya10@gmail.com


A.
Akrami
Chemistry,Arak Branch, Islamic Azad University
Chemistry,Arak Branch, Islamic Azad University
I R Iran
aahmad.akramii@gmail.com
QSAR
1Phenyl[2H]tetrahydrotriazine3oneanalogues
MLR
LSSVM
Threecenter Harary index and its applications
2
2
The Harary index H can be viewed as a molecular structure descriptor composed of increments representing interactions between pairs of atoms, such that their magnitude decreases with the increasing distance between the respective two atoms. A generalization of the Harary index, denoted by Hk, is achieved by employing the Steinertype distance between ktuples of atoms. We show that the linear combination H+x H3 is significantly better correlated with a variety of physicochemical properties of alkanes than H itself.
1

61
68


B.
Furtula
Faculty of Science, University of Kragujevac
Faculty of Science, University of Kragujevac
Serbia
boris.furtula@gmail.com


I.
Gutman
Faculty of Science, University of Kragujevac, Kragujevac, Serbia
Faculty of Science, University of Kragujevac,
Serbia
gutman@kg.ac.rs


V.
Katanic
Faculty of Science, University of Kragujevac
Faculty of Science, University of Kragujevac
Serbia
vlada.karanic@gmail.com
Harary index
Multicenter Harary index
Steiner distance
Molecular Graph
Investigation the effect of nanocomposite material on permeation flux of polyerthersulfone membrane using a mathematical approach
2
2
Integrally skinned asymmetric membranes based on nanocompositepolyethersulfone were prepared by the phase separation process using the supercritical CO2 as a nonsolvent for the polymer solution. In present study, the effects of temperature and nanoparticle on selectivity performance and permeability of gases has beeninvestigated. It is shown that the presence of silica nanoparticles not only disrupts the original polymer chain packing but also alters the chemical affinities of penetrants in polyethersulfone matrices. Because, in the presence of hydrophilic silica, CO2 affinity filler, hydrogenbond interactions between the oxygen atoms of carbon dioxide and the hydrogen atoms of hydroxyl group on the nanosilica surface would take place at the interface and thus solubility and consequently permeability towards CO2 are higher in comparison with CH4 for the membranes. Furthermore, in present study, a novel mathematical approach has been proposed to develop a model for permeation flux and selectivity performance of the membrane using Support Vector Machine. SVM is employed to develop a model toestimateprocess output variables of a nanocomposite membrane including permeation flux and selectivity performance. Model development that consists of training, optimization and test was performed using randomly selected 80%, 10%, and 10% of available data respectively.
1

69
75


M.
Adib
Payame Noor University (PNU)
Payame Noor University (PNU)
I R Iran
marjan_ad_1360@yahoo.com
Nanocomposite material • Polyerthersulfone membrane • Silica nanoparticles • Support Vector Machine (SVM)
On the generalized mass transfer with a chemical reaction: Fractional derivative model
2
2
In this article using the inverse Laplace transform, we show analytical solutions for the generalized mass transfers with (and without) a chemical reaction. These transfers have been expressed as the Couette flow with the fractional derivative of the Caputo sense. Also, using the Hankel contour for the Bromwich's integral, the solutions are given in terms of the generalized Airy functions.
1

77
88


A.
Ansari
Shahrekord University, P.O.Box 115, Shahrekord, Iran
Shahrekord University, P.O.Box 115, Shahrekord,
I R Iran
alireza_1038@yahoo.com


M.
Ahmadi Darani
Department of Applied Mathematics, Faculty of Mathematical Sciences,
Shahrekord University, P.O.Box 115, Shahrekord, Iran
Department of Applied Mathematics, Faculty
I R Iran
farshidahmadi633@gmail.com
Lévêque Problem
Laplace transform
Generalized Airy functions
Fractional derivative
A note on hyperZagreb index of graph operations
2
2
In this paper, the Hyper  Zagreb index of the Cartesian product, composition and corona product of graphs are computed. These corrects some errors in G. H. Shirdel et al.[11].
1

89
92


B.
Basavanagoud
KARNATAK UNIVERSITY DHARWAD
KARNATAK UNIVERSITY DHARWAD
India
b.basavanagoud@gmail.com


S.
Patil
KARNATAK UNIVERSITY, DHARWAD
KARNATAK UNIVERSITY, DHARWAD
India
shreekantpatil949@gmail.com
HyperZagreb index
Zagreb index
Graph operation
QSPR study on benzene derivatives to some physicochemical properties by using topological indices
2
2
QSPR study on benzene derivatives have been made using recently introduced topological methodology. In this study the relationship between the Randic' (x'), Balaban (J), Szeged (Sz),Harary (H), Wiener (W), HyperWiener and Wiener Polarity (WP) to the thermal energy (Eth), heat capacity (CV) and entropy (S) of benzene derivatives is represented. Physicochemical properties are taken from the quantum mechanics methodology with HF level using the ab initio 631G basis sets. The multiple linear regressions (MLR) and back ward methods (with significant at the 0.05 level) were employed to give the QSPR models. The satisfactory obtained results show that combining the two descriptors (Sz, HW) are useful topological descriptors for predicted (CV) and (S) of the 45 benzene derivatives. The training set models established by MLR method have not good correlation of (Eth), which means QSPR models could not predict the thermal energy of compounds.
1

93
110


M.
Pashm Forush
Islamic Azad Univ
Islamic Azad Univ
I R Iran


F.
Shafiei
Islamic Azad Univ
Islamic Azad Univ
I R Iran
shafa38@yahoo.com


F.
Dialamehpour
Islamic Azad Univ
Islamic Azad Univ
I R Iran
fd200988@yahoo.com
QSPR
Topological indices
Benzene derivatives
Graph theory
Multiple linear regressions (MLR)