Mixed extension concept as a tool for the spectral chararterization of graph

In this thesis, the use of the concept of mixed broadening has been examined in order to characterize graphs according to their spectra. In addition, the results available in the literature related to classification and spectral characterization of graphs with at most three eigenvalues different from -1 or 0 are given. This thesis consists of six chapters. In the first chapter, information about the subject, purpose and method of the thesis is given. In the second part, some basic definitions and concepts are given and the necessary background information is mentioned in the following sections. In the third chapter, the findings in the literature about graphs with at most two eigenvalues different from -1 or 0, which are the first part of the examined set, are given. In the fourth chapter, the findings in the literature regarding the graphs with exactly three eigenvalues different from -1 and 0, which are the other part of the examined cluster, are mentioned. In the fifth chapter, the mixed expansions of the three-point path graph and the full spectral characterizations of the pineapple graphs, which is a special case, are given. In the last chapter, which is the sixth chapter, the inferences and suggestions made as a result of the thesis work are mentioned.