2 Eigenvalues of graphs 5 2.1 Matrices associated with graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 The largest eigenvalue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.1 Adjacency matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.2 Laplacian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.3...

The study of eigenvalues of graphs has a long history. Since the early days, representation theory and number theory have been very useful for examining the spectra of strongly regular graphs with symmetries. In contrast, recent developments in spectral graph theory concern the effectiveness of eigenvalues in studying general (unstructured) graphs. The concepts and techniques, in large part, us...