The P3 Intersection Graph

We define a new graph operator called the P3 intersection graph, P3(G)- the intersection graph of all induced 3-paths in G. A characterization of graphs G for which P-3 (G) is bipartite is given . Forbidden subgraph characterization for P3 (G) having properties of being chordal , H-free, complete are also obtained . For integers a and b with a > 1 and b > a - 1, it is shown that there exists a graph G such that X(G) = a, X(P3( G)) = b, where X is the chromatic number of G. For the domination number -y(G), we construct graphs G such that -y(G) = a and -y (P3(G)) = b for any two positive numbers a > 1 and b. Similar construction for the independence number and radius, diameter relations are also discussed.

The Edge C4 Graph of a Graph

Abstract. The edge C4 graph E4(G) of a graph G has all the edges of Gas its vertices, two vertices in E4(G) are adjacent if their corresponding edges in G are either incident or are opposite edges of some C4. In this paper, characterizations for E4(G) being connected, complete, bipartite, tree etc are given. We have also proved that E4(G) has no forbidden subgraph characterization. Some dynamical behaviour such as convergence, mortality and touching number are also studied

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.

Studies on some graph operators and related topics

Department of Mathematics, Cochin University of Science and Technology

Electron-Phonon Interaction Within the Framework of the Fluctuating Valence of Copper Atoms — a Theoretical Model for High Temperature Superconductivity

Electron-phonon interaction is considered within the framework of the fluctuating valence of Cu atoms. Anderson's lattice Hamiltonian is suitably modified to take this into account. Using Green's function technique tbe possible quasiparticle excitations' are determined. The quantity 2delta k(O)/ kB Tc is calculated for Tc= 40 K. The calculated values are in good agreement with the experimental results.

Development of Shape Descriptors Based on Legendre Polynomials and Content-Based Retrieval of Scoliosis Images

The wealth of information available freely on the web and medical image databases poses a major problem for the end users: how to find the information needed? Content –Based Image Retrieval is the obvious solution.A standard called MPEG-7 was evolved to address the interoperability issues of content-based search.The work presented in this thesis mainly concentrates on developing new shape descriptors and a framework for content – based retrieval of scoliosis images.New region-based and contour based shape descriptor is developed based on orthogonal Legendre polymomials.A novel system for indexing and retrieval of digital spine radiographs with scoliosis is presented.

Studies on Some Graph Classes

Department of Mathematics, Cochin University of Science and Technology

Studies on some generalizations of line graph and the power domination problem in graphs

Department of Mathematics, Cochin University of Science and Technology

Theoretical study of the fluorinating power of SF6 to vanadocene

Màster Oficial en Química Teòrica i Computacional Curs: 2008-2009, Director: Juan J. Novoa Vide

Some non- linear problems in theoretical physics

An immense variety of problems in theoretical physics are of the non-linear type. Non~linear partial differential equations (NPDE) have almost become the rule rather than an exception in diverse branches of physics such as fluid mechanics, field theory, particle physics, statistical physics and optics, and the construction of exact solutions of these equations constitutes one of the most vigorous activities in theoretical physics today. The thesis entitled ‘Some Non-linear Problems in Theoretical Physics’ addresses various aspects of this problem at the classical level. For obtaining exact solutions we have used mathematical tools like the bilinear operator method, base equation technique and similarity method with emphasis on its group theoretical aspects. The thesis deals with certain methods of finding exact solutions of a number of non-linear partial differential equations of importance to theoretical physics. Some of these new solutions are of relevance from the applications point of view in diverse branches such as elementary particle physics, field theory, solid state physics and non-linear optics and give some insight into the stable or unstable behavior of dynamical Systems The thesis consists of six chapters.

Theoretical Studies on Air Pollution Meteorology in South India

Man's inadvertent interference with the environment by way of indiscreL¢ industrflflization has led to the deteriorating air quality in the recent times. The search is on to find the remedies to confine the air pollution levels with in their thershold limits. Theoretical studies play A crucial role in the control and for abatment of air pollution. Improper siting of industry is one of the most common reasons for the increased levels of air pollution in urban environments. A proper and effective ecological planning is an essential first step for any region in order to reduce the effects of air pollution. By means of theoretical models one can obtain the pollutant distribution in any urban area, provided the necessary data are available with the help of which the sites for new industries could be suggested, given the emission inventory. Studies on air pollution meteorology serve and aid the planners to initate remedial actions to bring down the levels of pollution and also to out—line the control strategy. In the present thesis some theoretical studies on air pollution meteorology over South India are made. The thesis is divided into six chapters