About this book
This book provides an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. It covers standard topics such as bounds on the sizes of cliques and cocliques, chromatic number and Shannon capacity, the connection between randomness and the 'eigenvalue gap', and applications. It continues with a presentation of some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics. Exercises at the end of each chapter provide practice and vary from easy yet interesting applications of the treated theory, to little excursions into related topics. Tables, references at the end of the book, an author and subject index enrich the text.
Spectra of Graphs is written for researchers, teachers and students interested in graph spectra. The reader is assumed to be familiar with basic linear algebra and eigenvalues, although some more advanced topics in linear algebra, like the Perron-Frobenius theorem and eigenvalue interlacing are included.
- DOI https://doi.org/10.1007/978-1-4614-1939-6
- Copyright Information Andries E. Brouwer and Willem H. Haemers 2012
- Publisher Name Springer, New York, NY
- eBook Packages Mathematics and Statistics
- Print ISBN 978-1-4614-1938-9
- Online ISBN 978-1-4614-1939-6
- Series Print ISSN 0172-5939
- Series Online ISSN 2191-6675
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