2015
6
1
1
92
Bounds for the CoPI index of a graph
2
2
In this paper, we present some inequalities for the CoPI index involving the some topological indices, the number of vertices and edges, and the maximum degree. After that, we give a result for trees. In addition, we give some inequalities for the largest eigenvalue of the CoPI matrix of G.
1

1
13


E.
Kaya
Igdir University
Science and Literature Faculty
Department of Mathematics
Igdir University
Science and Literature Faculty
De
Turkey
kaya_ezgi@windowslive.com


A. D.
Maden
Selcuk University
Science Faculty
Department of Mathematics
Selcuk University
Science Faculty
Department
Turkey
aysedilekmaden@selcuk.edu.tr
CoPI index
CoPI matrix
CoPI spectral radius
Relationship between topological indices and thermodynamic properties and of the monocarboxylic acids applications in QSPR
2
2
Topological indices are the numerical value associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. Graph theory is a delightful playground for the exploration of proof techniques in Discrete Mathematics and its results have applications in many areas of sciences. One of the useful indices for examination of structure property relationship is Randic' index. In this study is represented the relationship between the Randic', Balaban and Szeged indices and Harary numbers to the enthalpies of combustion ( liquid), enthalpies of vaporization( gas), enthalpies of formation ( liquid) and enthalpies of sublimation ( ) of monocarboxylic acids (C2 C20) are established, and then, some useful topological indices for examination of the structure property relationship are presented.
1

15
28


F.
Shafiei
Department of Chemistry, Science Faculty, Arak Branch, Islamic Azad University, Arak, Iran
Department of Chemistry, Science Faculty,
I R Iran
shafa38@yahoo.com
Topological indices
Graph theory
Monocarboxylic acid
QSPR
On the distance based indices of Hphenylenic nanotorus
2
2
Let G be a connected simple (molecular) graph. The distance d(u, v) between two vertices u and v of G is equal to the length of a shortest path that connects u and v. In this paper we compute some distance based topological indices of HPhenylenic nanotorus. At first we obtain an exact formula for the Wiener index. As application we calculate the Schultz index and modified Schultz index of this graph by using the Wiener index. Finally we compute eccentric connectivity index of this graph
1

29
39


A.
Heydari
Department of Science, Arak University of Technology, Arak, Iran
Department of Science, Arak University of
I R Iran
aheidari@iauarak.ac.ir
Wiener index
Schultz index
Modified Schultz index
eccentric connectivity index
HPhenylenic Nanotorus
On the harmonic index and harmonic polynomial of Caterpillars with diameter four
2
2
The harmonic index H(G) , of a graph G is defined as the sum of weights 2/(deg(u)+deg(v)) of all edges in E(G), where deg (u) denotes the degree of a vertex u in V(G). In this paper we define the harmonic polynomial of G. We present explicit formula for the values of harmonic polynomial for several families of specific graphs and we find the lower and upper bound for harmonic index in Caterpillars withf diameter 4.
1

41
49


M.
Iranmanesh
Department of Mathematics, Yazd University, 89195741, Yazd, Iran
Department of Mathematics, Yazd University,
I R Iran
iranmanesh@yazd.ac.ir


M.
Saheli
Department of Mathematics, Yazd University, 89195741, Yazd, Iran
Department of Mathematics, Yazd University,
I R Iran
mahboubeh.saheli@gmail.com
Harmonic index
Harmonic polynomial
Randić index
A new approach to compute acyclic chromatic index of certain chemical structures
2
2
An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph $G$ denoted by $chi_a '(G)$ is the minimum number $k$ such that there is an acyclic edge coloring using $k$ colors. The maximum degree in $G$ denoted by $Delta(G)$, is the lower bound for $chi_a '(G)$. $P$cuts introduced in this paper acts as a powerful tool to prove that this bound is sharp for certain chemical structures.
1

51
61


I.
Rajasingh
School of Advanced Sciences, VIT University, Chennai600127, India
School of Advanced Sciences, VIT University,
India
indrarajasingh@yahoo.co.in


R.
Rajan
School of Advanced Sciences, VIT University, Chennai600127, India
School of Advanced Sciences, VIT University,
India
vprsundar@gmail.com


D.
Paul
School of Advanced Sciences, VIT University, Chennai600127, India
School of Advanced Sciences, VIT University,
India
paul.d.joe@gmail.com
Acyclic edgecoloring
Acyclic chromatic index
Maximum degree
Certain chemical structures
The matching interdiction problem in dendrimers
2
2
The purpose of the matching interdiction problem in a weighted graph is to find two vertices such that the weight of the maximum matching in the graph without these vertices is minimized. An approximate solution for this problem has been presented. In this paper, we consider dendrimers as graphs such that the weights of edges are the bond lengths. We obtain the maximum matching in some types of dendrimers. Then, it is shown that proportion of difference of two optimal and approximate answers from the weight of maximum matching in these dendrimers is equal to the maximum value.
1

63
79


G.
Shirdel
University of Qom
University of Qom
I R Iran
shirdel81math@gmail.com


N.
Kahkeshani
Ph.D. Student at University of Qom
Ph.D. Student at University of Qom
I R Iran
nasrinkahkeshani@gmail.com
Matching
Interdiction
Dendrimer
Dynamical behavior and synchronization of chaotic chemical reactors model
2
2
In this paper, we discuss the dynamical properties of a chemical reactor model including Lyapunov exponents, bifurcation, stability of equilibrium and chaotic attractors as well as necessary conditions for this system to generate chaos. We study the synchronization of chemical reactors model via sliding mode control scheme. The stability of proposed method is proved by Barbalate’s lemma. Numerical Simulation is provided for illustration and verification of the proposed method.
1

81
92


H.
Kheiri
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
Faculty of Mathematical Sciences, University
I R Iran
hkheiri@tabrizu.ac.ir


B.
Naderi
Payame Noor university
Payame Noor university
I R Iran
b_naderi@pnu.ac.ir
Chemical reactor
chaos
Synchronization
Sliding mode