ABSTRACT
In this chapter, we look at the properties of graphs from our knowledge of their eigenvalues. The set of eigenvalues (with their multiplicities) of a graph G is the spectrum of its adjacency matrix and it is the spectrum of G and denoted by Sp(G). We compute the spectra of some well-known families of graphs-the family of complete graphs, the family of cycles, and so forth. We present Sachs’ theorem on the spectrum of the line graph of a regular graph. We also obtain the spectra of product graphs-Cartesian product, direct product, and strong product of two graphs.
