Introduction to Graph Theory

Name: Introduction to Graph Theory
Price: 8.01 USD
Availability: InStock
ISBN: 9780486678702

ISBN-10: 0486678709

ISBN-13: 9780486678702

Edition: 2nd 1993 (Reprint)

Authors: Richard J. Trudeau

List price: $16.95

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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 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.

Book details

List price: $16.95
Edition: 2nd
Copyright year: 1993
Publisher: Dover Publications, Incorporated
Publication date: 2/9/1994
Binding: Paperback
Pages: 240
Size: 0.47" wide x 8.54" long x 0.50" tall
Weight: 0.484
Language: English

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