Abstract: In this chapter, we look at the properties of graphs from our knowledge of their eigenvalues. The set of eigenvalues of a graph G is known as 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 etc. 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. We introduce Cayley graphs and Ramanujan graphs and highlight their importance. Finally, as an application of graph spectra to chemistry, we discuss the “energy of a graph”—a graph invariant that is widely studied these days. All graphs considered in this chapter are finite, undirected, and simple.
Publication Year: 2012
Publication Date: 2012-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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