Upper Saddle River, NJ 07458 All rights reserved. Riccardi Executive Managing Editor: Kathleen Schiaparelli Senior Managing Editor: Linda Mihatov Behrens Manufacturing Buyer: Alan Fischer Manufacturing Manager: Trudy Pisciotti Marketing Manager: Angela Battle Assistant Editor of Media: Vince Jansen Managing Editor, Audio/Video Assets: Grace Hazeldine Creative Director: Carole Anson Paul Belfanti: Director of Creative Services Interior/Cover Designer: John Christiana Art Director: Maureen Eide Editorial Assistant: Melanie Van Benthuysen Cover Image: Wassily Kandinsky, "Entwurf zu Kreise im Kreis" 1923, Philadelphia Museum of Art/ Corbis/Artists Right Society, NYġ998 by Prentice-Hall, Inc. QA39.3.G66 2002 511 -dc2l 2001037448 Acquisitions Editor: George Lobell Production Editor/Assistant Managing Editor: Bayani Mendoza de Leon Vice-President/Director of Production and Manufacturing: David W. Includes bibliographical references and index. Discrete mathematics with graph theory / Edgar G. Library of Congress Cataloging-in-Publication Data PRENTICE HALL Upper Saddle River, NJ 07458 Parmenter Memorial University of Newfoundland Goodaire Memorial University of Newfoundland The natural numbers the rational numbers the real numbers the integers the complex numbers the positive real numbersĭiscrete Mathematics with Graph Theory Second EditionĮdgar G. If and only if negation for all there exists and or denotes logical equivalence contradiction Used to express the negation of any symbol over which it is written for example,, means "does not belong to" used to denote the end of a proof the absolute value of x pronounced "aleph naught," this is the cardinality of the natural numbers approximately sum product Page numbers give the location of first appearance. Notation Here, and on the last two end papers, is a list of the symbols and other notation used in this book grouped, as best as possible, by subject. Represent this situation with a graph.Discrete Mathematices witLh Graph Thoery Second EditionĮdgar G. It turns out that Al and Cam are friends, as are Bob and Dan. The site allows members to be “friends” with each other. Īl, Bob, Cam, Dan, and Euler are all members of the social networking website Facebook. But first, here are a few other situations you can represent with graphs: Example 4.0.1. We will return to the question of finding paths through graphs later. All that matters is which land masses are connected to which other land masses, and how many times. It does not matter how big the islands are, what the bridges are made out of, if the river contains alligators, etc. We have distilled the “important” parts of the bridge picture for the purposes of the problem. ![]() The nice thing about looking at graphs instead of pictures of rivers, islands and bridges is that we now have a mathematical object to study. When two vertices are connected by an edge, we say they are adjacent. Graphs are made up of a collection of dots called vertices and lines connecting those dots called edges. Pictures like the dot and line drawing are called graphs. Any path in the dot and line drawing corresponds exactly to a path over the bridges of Königsberg. ![]() There is an obvious connection between these two problems.
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