The General Methods Of Studying The Spectra Of Graph

Recently, more and more scholars are devoted themselves to the research of the theory of graph spectra. For its widespread applications in the fields of statistical mechanics, com-munication network, computer science and quantum chemistry, spectral graph theory has become a very important research area in graph theory. Spectral graph theory consists of matrices and its associated graph. It is a mathematical theory where linear algebra and graph theory meet together. It is a theory in which graphs are studied by means of eigenvalues of a matrix which is in a prescribed way defined for any graph. Such matrices are the adjacency matrix, the incidence matrix, the diagonal matrix, the Laplacian matrix, the signless Laplacian matrix, the distance matrix and so on. In this paper, we give an almost completely summary of the research tools and methods among all over the world for the spectra by indexing, intensive reading, translating, classifying and organizating. The first chapter is background introduction and the concept of the spectra theory. The second chapter mainly lists the general utilization tools in the spectral research. The universal methods of the spectral research are shown in the third chapter.