Introduction to Graph Theory

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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.

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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: 9780486678702
  • Publisher: Dover Publications
  • Publication date: 2/9/1994
  • Edition number: 2
  • Pages: 240
  • Sales rank: 175,641
  • Series: Dover Books on Advanced Mathematics
  • Product dimensions: 5.38 (w) x 8.45 (h) x 0.45 (d)

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

Customer Reviews

Average Rating 4
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Sort by: Showing all of 4 Customer Reviews
  • Anonymous

    Posted September 26, 2009

    Very Interesting

    I am greatly enjoying this book. While it is not the final authority on this subject, it is not meant to be. It is a very good introduction to graph theory and a very interesting read.

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  • Anonymous

    Posted September 17, 2009

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    Posted May 7, 2009

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    Posted January 18, 2010

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