Spectra of Graphs
Springer Science & Business Media, Dec 17, 2011 - Mathematics - 250 pages
This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting 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 graduate 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.
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Chapter 2 Linear Algebra
Chapter 3 Eigenvalues and Eigenvectors of Graphs
Chapter 4 The SecondLargest Eigenvalue
Chapter 5 Trees
Chapter 6 Groups and Graphs
Chapter 7 Topology
Chapter 8 Euclidean Representations
Chapter 9 Strongly Regular Graphs
Chapter 10 Regular Twographs