Introduction to Graph Theory

Introduction to Graph Theory

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A stimulating excursion into pure mathematics aimed at "the mathematically traumatized," but great fun for mathematical hobbyists and serious mathematicians as well. Requiring only high school algebra as mathematical background, the 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, and a discussion of The Seven Bridges of Konigsberg. Exercises are included at the end of each chapter. "The topics are so well motivated, the exposition so lucid and delightful, that the book's appeal should be virtually universal . . . Every library should have several copies" "Choice." 1976 edition."show more

Product details

  • Paperback | 240 pages
  • 134.62 x 210.82 x 12.7mm | 249.47g
  • Dover Publications Inc.
  • New York, United States
  • English
  • Revised
  • 2nd Revised edition
  • 160ill.
  • 0486678709
  • 9780486678702
  • 64,635

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 symbolsshow more