Laplacian Eigenvectors of Graphs Perron-Frobenius and Faber-Krahn Ty
Eigenvectors of graph Laplacians have not, to date, been the subject of expository articles and thus they may seem a surprising topic for a book. The authors propose two motivations for this new LNM volume: (1) There are fascinating subtle differences bet
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Türker Bıyıkog˘lu Josef Leydold Peter F. Stadler
Laplacian Eigenvectors of Graphs Perron-Frobenius and Faber-Krahn Type Theorems
1915
Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
1915
Türker Bıyıko˘glu · Josef Leydold Peter F. Stadler
Laplacian Eigenvectors of Graphs Perron-Frobenius and Faber-Krahn Type Theorems
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Authors Türker Bıyıko˘glu
Josef Leydold
Department of Mathematics Faculty of Arts and Sciences I¸sık University Sile ¸ 34980, Istanbul Turkey e-mail: [email protected] URL: http://math.isikun.edu.tr/turker
Department of Statistics and Mathematics Vienna University of Economics and Business Administration Augasse 2-6 1090 Wien Austria e-mail: [email protected] URL: http://statmath.wu-wien.ac.at/˜ leydold/
Peter F. Stadler Bioinformatics Group Department of Computer Science University of Leipzig Härtelstrasse 16-18 04107 Leipzig Germany e-mail: [email protected] URL: http://www.bioinf.uni-leipzig.de
Library of Congress Control Number: 2007929852 Mathematics Subject Classification (2000): 05C50, 05C05, 05C35, 05C75, 15A18, 05C22
ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 ISBN 978-3-540-73509-0 Springer Berlin Heidelberg New York DOI 10.1007/978-3-540-73510-6 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2007 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting by the authors and SPi using a Springer LATEX macro package Cover design: design & production GmbH, Heidelberg Printed on acid-free paper
SPIN: 12087976
41/SPi
543210
Preface
Eigenvectors of graph Laplacians are a rather esoteric topic for a book. In fact, we are not aware of even a single review or survey article dedicated to this topic. We have, however, two excuses: (1) There are fascinating subtle differences between the properties of solutions of Schr¨ odinger equations on manifolds on the one hand, and their discrete analogs on graphs. (2) “Geometric” properties of (cost) functions defined on the vertex sets of graphs are of practical interest for heuristic optimization algorithms. Lov Grover’s observation that the cost functions of quite a few of the w
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