2014
5
1
1
0
Laplacian Energy of a Fuzzy Graph
2
2
A concept related to the spectrum of a graph is that of energy. The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of the adjacency matrix of G . The Laplacian energy of a graph G is equal to the sum of distances of the Laplacian eigenvalues of G and the average degree d(G) of G. In this paper we introduce the concept of Laplacian energy of fuzzy graphs. Let G be a fuzzy graph with n vertices and m edges. The Laplacian spectrum of fuzzy graph G is defined. The Laplacian energy of G has been recently defined . Section 2 consists of preliminaries and definition of Laplacian energy of a fuzzy graph and in Section 3, we present some results on Laplacian energy of a fuzzy graph. Some bounds o Laplacian energy of fuzzy graphs are also given.
1

1
10


S.
RAHIMI SHARBAF
University of Shahrood, I R Iran
University of Shahrood, I R Iran
I R Iran
srahimi40@yahoo.co.uk


F.
FAYAZI
University of Shahrood, I R Iran
University of Shahrood, I R Iran
I R Iran
fatemeh_victory@yahoo.com
Fuzzy graph
Fuzzy laplacian matrix
Laplacian spectrum
Laplacian energy of fuzzy graph
Computing Multiplicative Zagreb Indices with Respect to Chromatic and Clique Numbers
2
2
The chromatic number of a graph G, denoted by χ(G), is the minimum number of colors such that G can be colored with these colors in such a way that no two adjacent vertices have the same color. A clique in a graph is a set of mutually adjacent vertices. The maximum size of a clique in a graph G is called the clique number of G. The Turán graph Tn(k) is a complete kpartite graph whose partition sets differ in size by at most 1. The Wiener number [1] is the first reported distance based topological index and is defined as half sum of the distances between all the pairs of vertices in a molecular graph. Recently, some new versions of Zagreb indices are considered by mathematicians. In the present study we compute some bounds of multiplicative Zagreb indices and then we study these topological indices by using concept of chromatic number and clique number.
1

11
18


M.
GHORBANI
Department of mathematics, Shahid Rajaee Teacher Training University
Department of mathematics, Shahid Rajaee
I R Iran
mghorbani@srttu.edu


M.
SONGHORI
Department of Mathematics, Srtt University
Department of Mathematics, Srtt University
I R Iran
mahinsonghori@srttu.edu
Multiplicative Zagreb index
Clique number
Independence number
Chromatic number
Chemical Trees with Extreme Values of Zagreb Indices and Coindices
2
2
We give sharp upper bounds on the Zagreb indices and lower bounds on the Zagreb coindices of chemical trees and characterize the case of equality for each of these topological invariants.
1

19
29


Ž.
VUKIĆEVIĆ
University of Montenegro
University of Montenegro
Montenegro
zanak@cg.yu


G.
POPIVODA
Faculty of Natural Sciences and Mathematics, Department of Mathematics, University of Montenegro
Faculty of Natural Sciences and Mathematics,
Montenegro
goc@tcom.me
Zagreb index
Zagreb coindex
Chemical tree
Extensions to Study Electrochemical Interfaces  A Contribution to the Theory of Ions
2
2
In the present study an alternative model allows the extension of the DebyeHückel Theory (DHT) considering time dependence explicitly. From the ElectroQuasistatic approach (EQS) done in earlier studies time dependent potentials are suitable to describe several phenomena especially conducting media as well as the behaviour of charged particles in arbitrary solutions acting as electrolytes. This leads to a new formulation of the meaning of the nonlinear PoissonBoltzmann Equation (PBE). If a concentration and/or flux gradient of particles is considered the original structure of the mPBE will be modified leading to a new nonlinear partial differential equation (nPDE) of the third order. It is shown how one can derive classes of solutions for the potential function analytically by application of an algebraic method. The benefit of the mathematical tools used here is the fact that closedform solutions can be calculated without any numerical approximations.
1

31
46


A.
HUBER
A8062 Kumberg, Prottesweg 2a
A8062 Kumberg, Prottesweg 2a
Austria
dr.alfredhuber@gmx.at
Nonlinear partial differential equations
DebyeHückel Theory
PoissonBoltzmann Equation
Numerical Study on the Reaction Cum Diffusion Process in a Spherical Biocatalyst
2
2
In chemical engineering, several processes are represented by singular boundary value problems. In general, classical numerical methods fail to produce good approximations for the singular boundary value problems. In this paper, Chebyshev finite difference (ChFD) method and DTMPad´e method, which is a combination of differential transform method (DTM) and Pad´e approximant, are applied for solving singular boundary value problems arising in the reaction cum diffusion process in a spherical biocatalyst. ChFD method can be regarded as a nonuniform finite difference scheme and DTM is a numerical method based on the Taylor series expansion, which constructs an analytical solution in the form of a polynomial. The main advantage of DTM is that it can be applied directly to nonlinear ordinary without requiring linearization, discretization or perturbation. Therefore, it is not affected by errors associated to discretization. The results obtained, are in good agreement with those obtained numerically or by optimal homotopy analysis method.
1

47
61


A.
SAADATMANDI
University of Kashan
University of Kashan
I R Iran
a.saadatmandi@gmail.com


N.
NAFAR
University of Kashan
University of Kashan
I R Iran
nafiseh.nafar@yahoo.com


S. P.
TOUFIGHI
PACE Company, No.20, Pirouzan St., North Sheikh Bahaei Ave., Tehran, Iran
PACE Company, No.20, Pirouzan St., North
I R Iran
toufighi.p@paceco.net
DiffusionReaction
Biocatalyst
Effectiveness factor
Differential transform method
Chebyshev finite difference method
Eccentricity Sequence and the Eccentric Connectivity Index of Two Special Categories of Fullerenes
2
2
In this paper, we calculate the eccentric connectivity index and the eccentricity sequence of two infinite classes of fullerenes with 50 + 10k and 60 + 12k (k in N) carbon atoms.
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63
68


F.
KOOREPAZANMOFTAKHAR
Department of Pure Mathematics, Faculty of Mathematical Sciences,
University of Kashan, Kashan 8731751167, Iran
Department of Pure Mathematics, Faculty of
I R Iran
f.k.moftakhar@gmail.com


KH.
FATHALIKHANI
Department of Pure Mathematics, Faculty of Mathematical Sciences,
University of Kashan, Kashan 8731751167, Iran
Department of Pure Mathematics, Faculty of
I R Iran
fathalikhani.kh@ut.ac.ir
Eccentricity sequence
Eccentric connectivity index
Fullerene
A Characterization of the EntropyGibbs Transformations
2
2
Let h be a finite dimensional complex Hilbert space, b(h)+ be the set of all positive semidefinite operators on h and Phi is a (not necessarily linear) unital map of B(H) + preserving the EntropyGibbs transformation. Then there exists either a unitary or an antiunitary operator U on H such that Phi(A) = UAU* for any B(H) +. Thermodynamics, a branch of physics that is concerned with the study of heat (thermo) and power (dynamics), might at first seem more important for engineers trying to in vent a new engine than for biochemists trying to understand the mechanisms of life. However, since chemical reactions involve atoms and molecules that are bound by the laws of physics, studying thermodynamics should be a priority for every aspiring biochemist. There are two laws of thermodynamics that are important to the study of biochemistry. These two laws have to do with energy and order both essential for life as we know it. It is easy to understand that our bodies need energy to function from the visible muscle movement that gets us where we want to go, to the microscopic cellular processes that keep our brains thinking and our organs functioning. Order is also important. Our bodies represent a high degree of order: atoms and molecules are meticulously organized into a complex system ranging in scale from the microscopic to the macroscopic.
1

69
75


A.
SANAMI
Freelance Mathematics Researcher
Freelance Mathematics Researcher
I R Iran
a.sanami@yahoo.com
Preserver transformations
entropy
Rank one operator
Gibbs free energy