Introduction to Graph Theory

Introduction to Graph Theory

by Richard J. Trudeau
Introduction to Graph Theory

Introduction to Graph Theory

by Richard J. Trudeau

eBook

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Overview

A stimulating excursion into pure mathematics aimed at "the mathematically traumatized," but great fun for mathematical hobbyists and serious mathematicians as well. This book leads the reader from simple graphs through planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. Includes exercises. 1976 edition.

Product Details

ISBN-13: 9780486318660
Publisher: Dover Publications
Publication date: 03/18/2013
Series: Dover Books on Mathematics
Sold by: Barnes & Noble
Format: eBook
Pages: 224
File size: 9 MB

Table of Contents

Preface
1. Pure Mathematics
Introduction; Euclidean Geometry as Pure Mathematics; Games; Why Study Pure Mathematics?; What's Coming; Suggested Reading
2. Graphs
Introduction; Sets; Paradox; Graphs; Graph diagrams; Cautions; Common Graphs; Discovery; Complements and Subgraphs; Isomorphism; Recognizing Isomorphic Graphs; Semantics
The Number of Graphs Having a Given nu; Exercises; Suggested Reading
3. Planar Graphs
Introduction; UG, K subscript 5, and the Jordan Curve Theorem; Are there More Nonplanar Graphs?; Expansions;
Kuratowski's Theorem; Determining Whether a Graph is Planar or Nonplanar; Exercises; Suggested Reading
4. Euler's Formula
Introduction; Mathematical Induction; Proof of Euler's Formula; Some Consequences of Euler's Formula; Algebraic Topology; Exercises; Suggested Reading
5. Platonic Graphs
Introduction; Proof of the Theorem; History; Exercises; Suggested Reading
6. Coloring
Chromatic Number; Coloring Planar Graphs; Proof of the Five Color Theorem; Coloring Maps; Exercises; Suggested Reading
7. The Genus of a Graph
Introduction; The Genus of a Graph; Euler's Second Formula; Some Consequences; Estimating the Genus of a Connected Graph; g-Platonic Graphs; The Heawood Coloring Theorem; Exercises; Suggested Reading
8. Euler Walks and Hamilton Walks
Introduction; Euler Walks; Hamilton Walks; Multigraphs; The Königsberg Bridge Problem; Exercises; Suggested Reading
Afterword
Solutions to Selected Exercises
Index
Special symbols
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