Introduction to Graph Theory

    Introduction to Graph Theory

    By Richard J. Trudeau

    $16.95

    Publication Date: 9th February 1994

    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 s... Read More
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    Paperback
    1449 in stock
    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 s... Read More
    Description
    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.

    Reprint of Dots and Lines, The Kent State University Press, Kent, Ohio, 1976.
    Details
    • Price: $16.95
    • Pages: 224
    • Publisher: Dover Publications
    • Imprint: Dover Publications
    • Series: Dover Books on Mathematics
    • Publication Date: 9th February 1994
    • Trim Size: 5.5 x 8.5 in
    • ISBN: 9780486678702
    • Format: Paperback
    • BISACs:
      MATHEMATICS / Discrete Mathematics
      MATHEMATICS / Graphic Methods
    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
    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.

    Reprint of Dots and Lines, The Kent State University Press, Kent, Ohio, 1976.
    • Price: $16.95
    • Pages: 224
    • Publisher: Dover Publications
    • Imprint: Dover Publications
    • Series: Dover Books on Mathematics
    • Publication Date: 9th February 1994
    • Trim Size: 5.5 x 8.5 in
    • ISBN: 9780486678702
    • Format: Paperback
    • BISACs:
      MATHEMATICS / Discrete Mathematics
      MATHEMATICS / Graphic Methods
    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