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Introduction to Graph Theory 2nd Revised edition [Minkštas viršelis]

  • Formatas: Paperback / softback, 240 pages, aukštis x plotis x storis: 214x138x12 mm, weight: 260 g
  • Serija: Dover Books on Mathema 1.4tics
  • Išleidimo metai: 28-Mar-2003
  • Leidėjas: Dover Publications Inc.
  • ISBN-10: 0486678709
  • ISBN-13: 9780486678702
Kitos knygos pagal šią temą:
  • Formatas: Paperback / softback, 240 pages, aukštis x plotis x storis: 214x138x12 mm, weight: 260 g
  • Serija: Dover Books on Mathema 1.4tics
  • Išleidimo metai: 28-Mar-2003
  • Leidėjas: Dover Publications Inc.
  • ISBN-10: 0486678709
  • ISBN-13: 9780486678702
Kitos knygos pagal šią temą:
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.


Aimed at "the mathematically traumatized," this text offers nontechnical coverage of graph theory, with exercises. Discusses planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. 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