Graph energy

The aim of this work is to obtain new and original results on graph energy which is one of the most important application areas of graph theory. Graph energy appeared and fastly developed in the last 40 years. By means of linear algebraic methods, we can obtain mathematical values on the graphs and these values help us to comment on the molecular energies of the molecules under study. This PhD thesis consists of 6 chapters. The first section is organized as the Introduction. Fundamental notions and results which will be needed later on in the thesis are recalled here. In the second chapter, the material and methods used in the thesis are mentioned. In the third chapter, spectral polynomials of some specific graph classes are constructed and recurrence relations for these polynomials are obtained to find some formulae for the energy of these graph classes. In the fourth chapter, recurrence relations for the energy formulae obtained in the third chapter are established and some alternative energy recurrence relations to ease the calculations are given. In the fifth chapter, some new union operations on graphs, in the sixth chapter, subdivision operations for a graph are introduced and in these chapters, new techniques giving the spectral polynomials, their recurrence formulae and graph energy are established.