On spectral graph theory

In this thesis, graph operators, some graph types, matrix representations of graph structures and spectral properties of graphs are studied. The thesis consists of eight chapters. The first chapter presents the introduction and purpose of the thesis, the second chapter presents the literature survey related to the subject of the thesis. The third chapter introduces the basic concepts of graph theory. In the fourth chapter, some special structures of graphs such as trees, walks, paths, trips, cycles, etc., which are well known in the literature and are the basic components of graphs, are introduced. In the fifth section, connectivity in graphs is analyzed and examples of regular, directed and planar graph types are given. In the sixth section, the degree, adjacency, incidence and Laplacian matrix representations of graphs are studied and information about the spectral properties of graphs is given. In the seventh chapter, Laplacian spectral properties of finite projective planes of order 2 and 3, which are examples of k-uniform hypergraphs, are analyzed. The eighth chapter, which is the last chapter of the thesis, contains the conclusions and recommendations related to the thesis.