Graph theory with applications PDF
Preview Graph theory with applications
This page intentionally left blank Copyright © 2006 New Age International (P) Ltd., Publishers Published by New Age International (P) Ltd., Publishers All rights reserved. No part of this ebook may be reproduced in any form, by photostat, microfilm, xerography, or any other means, or incorporated into any information retrieval system, electronic or mechanical, without the written permission of the publisher. All inquiries should be emailed to [email protected] ISBN : 978-81-224-2413-3 PUBLISHING FOR ONE WORLD NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS 4835/24, Ansari Road, Daryaganj, New Delhi - 110002 Visit us at www.newagepublishers.com IIIII DDDDDeeeeedddddiiiiicccccaaaaattttteeeeeddddd ttttthhhhhiiiiisssss bbbbbooooooooookkkkk tttttooooo ‘‘‘‘‘MMMMMaaaaahhhhhaaaaa KKKKKaaaaaaaaaallllliiiii MMMMMaaaaaaaaaatttttaaaaa’’’’’ This page intentionally left blank PREFACE This text has been carefully designed for flexible use. It is primarily designed to provide an introduction to some fundamental concepts in Graph Theory, for under-graduate and post-graduate students. Each topic is divided into sections of approximately the same length, and each section is divided into subsections that form natural blocks of material for teaching. Instructors can easily pace their lectures using these blocks. All definitions and theorems in this text are stated extremely carefully so that students will ap- preciate the precision of language and rigor needed in mathematical sciences. Proofs are motivated and developed slowly ; their steps are all carefully justified. The writing style in this book is direct and pragmatic. Precise mathematical language is used without excessive formalism and abstraction. Care has been taken to balance the mix of notation and words in mathematical statements. Over 1500 problems are used to illustrate concepts, related to different topics, and introduce applications. In most examples, a question is first posed, then its solution is presented with appropriate details. The applications included in this text demonstrate the utility of Graph Theory, in the solution of real-world problem. This text includes applications to a wide-variety of areas, including computer science and engineering. There are over 1000 exercises in the text with many different types of questions posed. There is an ample supply of straightforward exercises that develop basic skills, a large number of intermediate exercises and many challenging exercise sets. Problem sets are stated clearly and unambiguously, and all are carefully graded for various levels of difficulty. It will be honest on my part to accept that it is not possible to include everything in one book. Many people contributed directly or indirectly to the completion of this book. Thanks are due to my friends who were able to convince me that I should write this book. I am grateful to my students, who always encouraged me and many times thanked me for writing this book. Special thanks to my teachers, who made me realize that I can indeed write a book on “Graph Theory”. Some pulled me down, some encouraged me and some gave me constructive suggestions. I am grateful to all of them. I specially thank my parents, elder brothers, elder sister and maternal uncle, who tolerated me all along while I devoted my time to completing this book. I experess my sincere thanks to the Chairman Mr. R.K. Gupta, the Managing Director Mr. Saumya Gupta, the Marketing Manager Mr. V.R. Babu and Mr. Vincent D. Souza, M/s New Age International (P) Ltd. Publishers, New Delhi, for their responsible work-done at every level in the publication of the book with high production standards. Healthy criticism and suggestions to improve the quality and standards of the text are most welcome. Bangalore C. Vasudev This page intentionally left blank This page intentionally left blank
The list of books you might like
