Geodesic Convexity in Graphs
Geodesic Convexity in Graphs is devoted to the study of the geodesic convexity on finite, simple, connected graphs. The first chapter includes the main definitions and results on graph theory, metric graph theory and graph path convexities. T
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Ignacio M. Pelayo
Geodesic Convexity in Graphs
123
SpringerBriefs in Mathematics
Series Editors Krishnaswami Alladi Nicola Bellomo Michele Benzi Tatsien Li Matthias Neufang Otmar Scherzer Dierk Schleicher Benjamin Steinberg Vladas Sidoravicius Yuri Tschinkel Loring W. Tu G. George Yin Ping Zhang
SpringerBriefs in Mathematics showcases expositions in all areas of mathematics and applied mathematics. Manuscripts presenting new results or a single new result in a classical field, new field, or an emerging topic, applications, or bridges between new results and already published works, are encouraged. The series is intended for mathematicians and applied mathematicians. For further volumes: http://www.springer.com/series/10030
Ignacio M. Pelayo
Geodesic Convexity in Graphs
123
Ignacio M. Pelayo School of Agricultural Engineering of Barcelona Barcelona, Spain
ISSN 2191-8198 ISSN 2191-8201 (electronic) ISBN 978-1-4614-8698-5 ISBN 978-1-4614-8699-2 (eBook) DOI 10.1007/978-1-4614-8699-2 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2013946414 Mathematics Subject Classification (2010): 05C12, 05C35 © Ignacio M. Pelayo 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, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
This monograph is intended to present the curr
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