E-Book Overview
Configurations can be studied from a graph-theoretical viewpoint via the so-called Levi graphs and lie at the heart of graphs, groups, surfaces, and geometries, all of which are very active areas of mathematical exploration. In this self-contained textbook, algebraic graph theory is used to introduce groups; topological graph theory is used to explore surfaces; and geometric graph theory is implemented to analyze incidence geometries.
After a preview of configurations in Chapter 1, a concise introduction to graph theory is presented in Chapter 2, followed by a geometric introduction to groups in Chapter 3. Maps and surfaces are combinatorially treated in Chapter 4. Chapter 5 introduces the concept of incidence structure through vertex colored graphs, and the combinatorial aspects of classical configurations are studied. Geometric aspects, some historical remarks, references, and applications of classical configurations appear in the last chapter.
With over two hundred illustrations, challenging exercises at the end of each chapter, a comprehensive bibliography, and a set of open problems, Configurations from a Graphical Viewpoint is well suited for a graduate graph theory course, an advanced undergraduate seminar, or a self-contained reference for mathematicians and researchers.
E-Book Content
Birkh¨auser Advanced Texts Series Editors Steven G. Krantz, Washington University, St. Louis Shrawan Kumar, University of North Carolina at Chapel Hill Jan Nekov´aˇr, Universit´e Pierre et Marie Curie, Paris
For further volumes: http://www.springer.com/series/4842
Tomaˇz Pisanski • Brigitte Servatius
Configurations from a Graphical Viewpoint
Tomaˇz Pisanski IMFM Oddelek za Teoretiˇcno Raˇcunalniˇstvo Univerza v Ljubljani Ljubljana, Slovenia
Brigitte Servatius Department of Mathematics Worcester Polytechnic Institute Worcester, MA, USA
ISBN 978-0-8176-8363-4 ISBN 978-0-8176-8364-1 (eBook) DOI 10.1007/978-0-8176-8364-1 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2012944998 Mathematics Subject Classification (2010): 05-01, 05Bxx, 05Cxx, 20-01, 51-01 © Springer Science+Business Media New York 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, expre