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Introduction to Graph Theory

ISBN-10: 0486678709
ISBN-13: 9780486678702
Edition: 2nd 1993 (Reprint)
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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  More...

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Book details

List price: $15.95
Edition: 2nd
Copyright year: 1993
Publisher: Dover Publications, Incorporated
Publication date: 2/9/1994
Binding: Paperback
Pages: 240
Size: 5.50" wide x 8.50" long x 0.50" tall
Weight: 0.484
Language: English

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.

Steven Watson is a cultural historian and documentary filmmaker. His other books includeStrange Bedfellows,The Harlem Renaissance,The Birth of the Beat Generation, andPrepare for Saints: Gertrude Stein,Virgil Thomson, and the Mainstreaming of American Modernism. He lives in New York City.

Preface
Pure Mathematics
Introduction
Euclidean Geometry as Pure Mathematics
Games
Why Study Pure Mathematics?
What's Coming
Suggested Reading
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
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
Euler's Formula
Introduction
Mathematical Induction
Proof of Euler's Formula
Some Consequences of Euler's Formula
Algebraic Topology
Exercises
Suggested Reading
Platonic Graphs
Introduction
Proof of the Theorem
History
Exercises
Suggested Reading
Coloring
Chromatic Number
Coloring Planar Graphs
Proof of the Five Color Theorem
Coloring Maps
Exercises
Suggested Reading
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
Euler Walks and Hamilton Walks
Introduction
Euler Walks
Hamilton Walks
Multigraphs
The Konigsberg Bridge Problem
Exercises
Suggested Reading
Afterword
Solutions to Selected Exercises
Index
Special symbols

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