Spectra of Graphs
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,
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Universitext is a series of textbooks that presents material from a wide variety of mathematical disciplines at master’s level and beyond. The books, often well class-tested by their author, may have an informal, personal even experimental approach to their subject matter. Some of the most successful and established books in the series have evolved through several editions, always following the evolution of teaching curricula, to very polished texts. Thus as research topics trickle down into graduate-level teaching, first textbooks written for new, cutting-edge courses may make their way into Universitext. For further volumes: http://www.springer.com/series/223
Andries E. Brouwer • Willem H. Haemers
Spectra of Graphs
Andries E. Brouwer Department of Mathematics Eindhoven University of Technology Eindhoven The Netherlands
Willem H. Haemers Department of Econometrics and Operations Research Tilburg University Tilburg The Netherlands
ISSN 0172-5939 e-ISSN 2191-6675 ISBN 978-1-4614-1938-9 e-ISBN 978-1-4614-1939-6 DOI 10.1007/978-1-4614-1939-6 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011944191 Mathematics Subject Classification (2010): 05Exx, 05Bxx, 05Cxx, 05Dxx, 15Axx, 51Exx, 94Bxx, 94Cxx © Andries E. Brouwer and Willem H. Haemers 2012 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
Algebraic graph theory is the branch of mathematics that studies graphs by using algebraic properties of associated matrices. In particular, spectral graph theory studies the relation between graph properties and the spectrum of the adjacency matrix or Laplace matrix. And the theory of association schemes and coherent configurations studies the algebra generated by associated matrices. Spectral graph theory is a useful subject. The founders of Google computed the Perron-Frobenius eigenvector of the web graph and became billionaire
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