A Note on Energy of Some Graphs

Eigenvalue of a graph is the eigenvalue of its adjacency matrix. The energy of a graph is the sum of the absolute values of its eigenvalues. In this note we obtain analytic expressions for the energy of two classes of regular graphs.

Equienergetic self-complementary graphs

In this paper equienergetic self-complementary graphs on p vertices for every p = 4k; k ¸ 2 and p = 24t + 1; t ¸ 3 are constructed

Some classes of Turker equivalent graphs

Two graphs G and H are Turker equivalent if they have the same set of Turker angles. In this paper some Turker equivalent family of graphs are obtained.

Studies on Some Simple and Zeolite-Y Encapsulated 3d-Transition Metal Complexes of Schiff Bases Derived From 2-Aminobenzothiazole

In this regard Schiff base complexes have attracted wide attention. Furthermore, such complexes are found to play important role in analytical chemistry, organic synthesis, metallurgy, refining of metals, electroplating and photography. Many Schiff base complexes are reported in literature. Their properties depend on the nature of the metal ion as well as on the nature of the ligand. By altering the ligands it is possible to obtain desired electronic environment around the metal ion. Thus there is a continuing interest in the synthesis of simple and zeolite encapsulated Schiff base complexes of metal ions. Zeolites have a number of striking structural similarities to the protein portion of natural enzymes. Zeolite based catalysts are known for their remarkable ability of mimicking the chemistry of biological systems. In view of the importance of catalysts in all the areas of modern chemical industries, an effort has been made to synthesize some simple Schiff base complexes, heterogenize them by encapsulating within the supercages of zeoliteY cavities and to study their applications. The thesis deals with studies on the synthesis and characterization of some simple and zeoliteY encapsulated Mn(II), Fe(III), Co(II), Ni(II) and Cu(II) complexes and on the catalytic activity of these complexes on some oxidation reactions. Simple complexes were prepared from the Schiff base ligands SBT derived from 2-aminobenzothiazole and salicylaldehyde and the ligand VBT derived from 2-aminobenzothiazole and vanillin (4-hydroxy-3- methoxybenzaldehyde). ZeoliteY encapsulated Mn(II), Fe(III), Co(II), Ni(II) and Cu(II) complexes of Schiff base ligands SBT and VBT and also of 2-aminobenzothiazole were synthesized. All the prepared complexes were characterized using the physico-chemical techniques such as chemical analysis (employing AAS and CHN analyses), magnetic moment studies, conductance measurements and electronic and FTIR spectra. EPR spectra of the Cu(II) complexes were also carried out to know the probable structures and nature of Cu(II) complexes. Thermogravimetric analyses were carried out to obtain the information regarding the thermal stability of various complexes. The successful encapsulations of the complexes within the cavities of zeoliteY were ascertained by XRD, surface area and pore volume analysis. Assignments of geometries of simple and zeoliteY encapsulated complexes are given in all the cases. Both simple and zeoliteY encapsulated complexes were screened for catalytic activity towards oxidation reactions such as decomposition of hydrogen peroxide, oxidation of benzaldehyde, benzyl alcohol, 1-propanol, 2-propanol and cyclohexanol.

Simple Low-cost Planar Antenna for Indoor Communication under the Bluetooth Protocol

A single-feed rectangular-ring microstrip antenna is proposed for indoor communication under the Bluetooth protocol. The dimensions of the antenna together with the location of the feed point are optimized through field simulations in order to cover the Bluetooth bandwidth and to avoid linear polarization. The performance and the efficiency of the antenna are illustrated in a real indoor environment

A Simple Free-Space Method for Measuring the Complex Permittivity of Single and Compound Dielectric Materials

A simple and efficient method for determining the complex permittivity of dielectric materials from both reflected and transmitted signals is presented. It is also novel because the technique is implemented using two pyramidal horns without any focusing mechanisms. The dielectric constant of a noninteractive and distributive (NID) mixture of dielectrics is also determined

The (t) property of some classes of graphs

In this note,the (t) properties of five class are studied. We proved that the classes of cographs and clique perfect graphs without isolated vertices satisfy the (2) property and the (3) property, but do not satisfy the (t) property for tis greater than equal to 4. The (t) properties of the planar graphs and the perfect graphss are also studied . we obtain a necessary and suffieient conditions for the trestled graph of index K to satisfy the (2) property

SOME NEW INTEGRAL GRAPHS

The eigenvalue of a graph is the eigenvalue of its adjacency matrix . A graph G is integral if all of its cigenvalues are integers. In this paper some new classes of integral graphs are constructed.

GALLAI AND ANTI-GALLAI GRAPHS OF A GRAPH

Abstract. The paper deals with graph operators-the Gallai graphs and the anti-Gallai graphs. We prove the existence of a finite family of forbidden subgraphs for the Gallai graphs and the anti-Gallai graphs to be H-free for any finite graph H. The case of complement reducible graphs-cographs is discussed in detail. Some relations between the chromatic number, the radius and the diameter of a graph and its Gallai and anti-Gallai graphs are also obtained.

Antimedian graphs

Antimedian graphs are introduced as the graphs in which for every triple of vertices there exists a unique vertex x that maximizes the sum of the distances from x to the vertices of the triple. The Cartesian product of graphs is antimedian if and only if its factors are antimedian. It is proved that multiplying a non-antimedian vertex in an antimedian graph yields a larger antimedian graph. Thin even belts are introduced and proved to be antimedian. A characterization of antimedian trees is given that leads to a linear recognition algorithm.

Energies of some non-regular graphs

The energy of a graph G is the sum of the absolute values of its eigenvalues. In this paper, we study the energies of some classes of non-regular graphs. Also the spectrum of some non-regular graphs and their complements are discussed.

Studies on the dynamics and rheology of dilute suspensions of Brownian particles in simple shear flow under the action of an external force

We present a novel approach to computing the orientation moments and rheological properties of a dilute suspension of spheroids in a simple shear flow at arbitrary Peclct number based on a generalised Langevin equation method. This method differs from the diffusion equation method which is commonly used to model similar systems in that the actual equations of motion for the orientations of the individual particles are used in the computations, instead of a solution of the diffusion equation of the system. It also differs from the method of 'Brownian dynamics simulations' in that the equations used for the simulations are deterministic differential equations even in the presence of noise, and not stochastic differential equations as in Brownian dynamics simulations. One advantage of the present approach over the Fokker-Planck equation formalism is that it employs a common strategy that can be applied across a wide range of shear and diffusion parameters. Also, since deterministic differential equations are easier to simulate than stochastic differential equations, the Langevin equation method presented in this work is more efficient and less computationally intensive than Brownian dynamics simulations.We derive the Langevin equations governing the orientations of the particles in the suspension and evolve a procedure for obtaining the equation of motion for any orientation moment. A computational technique is described for simulating the orientation moments dynamically from a set of time-averaged Langevin equations, which can be used to obtain the moments when the governing equations are harder to solve analytically. The results obtained using this method are in good agreement with those available in the literature.The above computational method is also used to investigate the effect of rotational Brownian motion on the rheology of the suspension under the action of an external force field. The force field is assumed to be either constant or periodic. In the case of con- I stant external fields earlier results in the literature are reproduced, while for the case of periodic forcing certain parametric regimes corresponding to weak Brownian diffusion are identified where the rheological parameters evolve chaotically and settle onto a low dimensional attractor. The response of the system to variations in the magnitude and orientation of the force field and strength of diffusion is also analyzed through numerical experiments. It is also demonstrated that the aperiodic behaviour exhibited by the system could not have been picked up by the diffusion equation approach as presently used in the literature.The main contributions of this work include the preparation of the basic framework for applying the Langevin method to standard flow problems, quantification of rotary Brownian effects by using the new method, the paired-moment scheme for computing the moments and its use in solving an otherwise intractable problem especially in the limit of small Brownian motion where the problem becomes singular, and a demonstration of how systems governed by a Fokker-Planck equation can be explored for possible chaotic behaviour.

Study on the determination of molecular distance in organic dye mixtures using dual beam thermal lens technique

A sensitive method based on the principle of photothermal phenomena to study the energy transfer processes in organic dye mixtures is presented. A dual beam thermal lens method can be very effectively used as an alternate technique to determine the molecular distance between donor and acceptor in fluorescein–rhodamine B mixture using optical parametric oscillator.

A simple linear magnetic field sweep generator for magnetic resonance experiments

A simple and inexpensive linear magnetic field sweep generating system suitable for magnetic resonance experiments is described. The circuit, utilising a modified IC bootstrap configuration, generates field sweep over a wide range of sweep durations with excellent sweep linearity.