Richard J. Trudeau

Introduction to Graph Theory (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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.

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Produktdetails

• Verlag: Dover Publications
• Seitenzahl: 224
• Erscheinungstermin: 15. April 2013
• Englisch
• ISBN-13: 9780486318660
• Artikelnr.: 39539184

Inhaltsangabe

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