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Viser: Introduction to Graph Theory

Introduction to Graph Theory

Richard J. Trudeau

(2003)

Sprog: Engelsk

Dover Publications, Incorporated

199,00 kr.

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2. Udgave
Paperback: 224 sider
Udgiver: Dover Publications, Incorporated (Marts 2003)
ISBN: 9780486678702

Beskrivelse
Indhold

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.

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