eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2016-03-01
7
1
1
9
10.22052/ijmc.2016.10845
10845
Degree distance index of the Mycielskian and its complement
A. Behtoei
a.behtoei@sci.ikiu.ac.ir
1
M. Anbarloei
m.anbarloei@sci.ikiu.ac.ir
2
Imam Khomeini International University
Imam Khomeini International University
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.
http://ijmc.kashanu.ac.ir/article_10845_4ba6f41aaf61461b68f1c3078233f5e5.pdf
Degree distance
Zagreb indices
Mycielskian
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2016-03-01
7
1
11
17
10.22052/ijmc.2016.11865
11865
A note on vertex-edge Wiener indices of graphs
M. Azari
mahdie.azari@gmail.com
1
Kazerun Branch, Islamic Azad University
The vertex-edge 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,e|G) and D_2(u,e|G) between a vertex u and an edge e of G were considered in the literature and according to them, the corresponding vertex-edge Wiener indices W_{ve_1}(G) and W_{ve_2}(G) were introduced. In this paper, we present exact formulas for computing the vertex-edge Wiener indices of two composite graphs named splice and link.
http://ijmc.kashanu.ac.ir/article_11865_9080447f4b5e8d2998640cb39bf045d7.pdf
Distance in graph
Vertex-edge Wiener index
Splice
Link
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2016-03-01
7
1
19
27
10.22052/ijmc.2016.11866
11866
Electro-spunorganic nanofibers elaboration process investigations using BPs operational matrices
H. Jafari
jafari@umz.ac.ir
1
H. Tajadodi
tajadodi@umz.ac.ir
2
University of Mazandaran
University of Sistan and Baluchestan
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 non-woven 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.
http://ijmc.kashanu.ac.ir/article_11866_914b2e89361dc43a0182ac89574aa076.pdf
Bratu equation
Elecotrospun nanofibers
Bernstein polynomials
operational matrix
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2016-03-01
7
1
29
38
10.22052/ijmc.2016.11867
11867
Hosoya polynomials of random benzenoid chains
S.-J. Xu
shjxu@lzu.edu.cn
1
Q.-H. He
heqh12@lzu.edu.cn
2
S. Zhou
zhous@lzu.edu.cn
3
W. Chan
waihchan@ied.edu.hk
4
Lanzhou University
Lanzhou University
Jiangsu Normal University
waihchan@ied.edu.hk
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 well-known topological indices: Wiener index, hyper-Wiener index and Tratch-Stankevitch-Zefirov 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) 403-408].
http://ijmc.kashanu.ac.ir/article_11867_e0847f53fd013808c54145717912481c.pdf
Wiener index
Random benzenoid chain
Hosoya polynomial
Expected value
Generating function
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2016-03-01
7
1
39
46
10.22052/ijmc.2016.11868
11868
Complete forcing numbers of polyphenyl systems
B. Liu
446297409@qq.com
1
H. Bian
bh_1218@sina.com
2
H. Yu
yhz0611@163.com
3
School of Mathematical Sciences, Xinjiang Normal University, Urumqi, Xinjiang 830054, P. R. China
Department of Mathematics, Xinjiang Normal University, Urumqi, Xinjiang 830054, P.R.China
College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, P.R.China
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.
http://ijmc.kashanu.ac.ir/article_11868_5eb2b2f068c3fbac354c9f2fde2cfdd1.pdf
Complete forcing number
Polyphenly system
Global forcing number
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2016-03-01
7
1
47
59
10.22052/ijmc.2016.11869
11869
Quantitative structure activity relationship study of inhibitory activities of 5-lipoxygenase and design new compounds by different chemometrics methods
F. Bagheban-Shahri
f.baghebanshahri@gmail.com
1
A. Niazi
chemistrya10@gmail.com
2
A. Akrami
aahmad.akramii@gmail.com
3
Chemistry,Arak Branch, Islamic Azad University
Chemistry,Arak Branch, Islamic Azad University
Chemistry,Arak Branch, Islamic Azad University
A quantitative structure-activity relationship (QSAR) study was conducted for the prediction of inhibitory activity of 1-phenyl[2H]-tetrahydro-triazine-3-one analogues as inhibitors of 5-Lipoxygenase. The inhibitory activities of the 1-phenyl[2H]-tetrahydro-triazine-3-one analogues modeled as a function of molecular structures using chemometrics methods such as multiple linear regression (MLR) and least squares support vector machines (LS-SVM). 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 LS-SVM, respectively. The LS-SVM method was used for prediction of inhibitory activity of the new inhibitor derivatives.
http://ijmc.kashanu.ac.ir/article_11869_1b5ded026dcd8a75a7cd052243b4ad72.pdf
QSAR
1-Phenyl[2H]-tetrahydro-triazine-3-oneanalogues
MLR
LS-SVM
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2016-03-01
7
1
61
68
10.22052/ijmc.2016.12402
12402
Three-center Harary index and its applications
B. Furtula
boris.furtula@gmail.com
1
I. Gutman
gutman@kg.ac.rs
2
V. Katanic
vlada.karanic@gmail.com
3
Faculty of Science, University of Kragujevac
Faculty of Science, University of Kragujevac, Kragujevac, Serbia
Faculty of Science, University of Kragujevac
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 Steiner-type distance between k-tuples of atoms. We show that the linear combination H+x H3 is significantly better correlated with a variety of physico-chemical properties of alkanes than H itself.
http://ijmc.kashanu.ac.ir/article_12402_ff64ec64188304a21bed1c7a4b1c22e4.pdf
Harary index
Multicenter Harary index
Steiner distance
Molecular Graph
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2016-03-01
7
1
69
75
10.22052/ijmc.2016.12403
12403
Investigation the effect of nanocomposite material on permeation flux of polyerthersulfone membrane using a mathematical approach
M. Adib
marjan_ad_1360@yahoo.com
1
Payame Noor University (PNU)
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, hydrogen-bond 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.
http://ijmc.kashanu.ac.ir/article_12403_a9874c07a28f1c3c7b67ab286aecd0d9.pdf
Nanocomposite material • Polyerthersulfone membrane • Silica nanoparticles • Support Vector Machine (SVM)
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2016-03-01
7
1
77
88
10.22052/ijmc.2016.12404
12404
On the generalized mass transfer with a chemical reaction: Fractional derivative model
A. Ansari
alireza_1038@yahoo.com
1
M. Ahmadi Darani
farshidahmadi633@gmail.com
2
Shahrekord University, P.O.Box 115, Shahrekord, Iran
Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iran
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.
http://ijmc.kashanu.ac.ir/article_12404_412497ee8587a49f897a821ff5f751f8.pdf
Lévêque Problem
Laplace transform
Generalized Airy functions
Fractional derivative
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2016-03-01
7
1
89
92
10.22052/ijmc.2016.12405
12405
A note on hyper-Zagreb index of graph operations
B. Basavanagoud
b.basavanagoud@gmail.com
1
S. Patil
shreekantpatil949@gmail.com
2
KARNATAK UNIVERSITY DHARWAD
KARNATAK UNIVERSITY, DHARWAD
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].
http://ijmc.kashanu.ac.ir/article_12405_2b6320568ffc299789173e21593336db.pdf
Hyper-Zagreb index
Zagreb index
Graph operation
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2016-03-01
7
1
93
110
10.22052/ijmc.2016.12410
12410
QSPR study on benzene derivatives to some physico-chemical properties by using topological indices
M. Pashm Forush
1
F. Shafiei
shafa38@yahoo.com
2
F. Dialamehpour
fd200988@yahoo.com
3
Islamic Azad Univ
Islamic Azad Univ
Islamic Azad Univ
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 6-31G 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.
http://ijmc.kashanu.ac.ir/article_12410_d4fb17c9ff5de612df4bd46f3053f2c6.pdf
QSPR
Topological indices
Benzene derivatives
Graph theory
Multiple linear regressions (MLR)