Spectra of graphs Andries E. Brouwer Willem H. Haemers 2 Contents 1 Graph spectrum 9 1.1 Matrices associated to a graph . . . . . . . . . . . . . . . . . . . 9 1.2 The spectrum of a graph . . . . . . . . . . . . . . . . . . . . . . . 10 1.2.1 Characteristic polynomial . . . . . . . . . . . . . . . . . . 11 1.3 The spectrum of an undirected graph . . . . . . . . . . . . . . . . 11 1.3.1 Regular gr