Introduction to Graph Theory

Häftad, Engelska, 2003

Del i serien Dover Books on Mathema 1.4tics

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Beskrivning

A stimulating excursion into pure mathematics aimed at "the mathematically traumatized," but great fun for mathematical hobbyists and serious mathematicians as well. This 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, more. Includes exercises. 1976 edition.

Produktinformation

Utgivningsdatum:2003-03-28
Mått:136 x 215 x 14 mm
Vikt:240 g
Format:Häftad
Språk:Engelska
Serie:Dover Books on Mathema 1.4tics
Antal sidor:224
Upplaga:94002
Förlag:Dover Publications Inc.
ISBN:9780486678702

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Innehållsförteckning

Preface1. Pure MathematicsIntroduction; Euclidean Geometry as Pure Mathematics; Games; Why Study Pure Mathematics?; What's Coming; Suggested Reading2. GraphsIntroduction; Sets; Paradox; Graphs; Graph diagrams; Cautions; Common Graphs; Discovery; Complements and Subgraphs; Isomorphism; Recognizing Isomorphic Graphs; SemanticsThe Number of Graphs Having a Given nu; Exercises; Suggested Reading3. Planar GraphsIntroduction; 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 Reading4. Euler's FormulaIntroduction; Mathematical Induction; Proof of Euler's Formula; Some Consequences of Euler's Formula; Algebraic Topology; Exercises; Suggested Reading5. Platonic GraphsIntroduction; Proof of the Theorem; History; Exercises; Suggested Reading6. ColoringChromatic Number; Coloring Planar Graphs; Proof of the Five Color Theorem; Coloring Maps; Exercises; Suggested Reading7. The Genus of a GraphIntroduction; 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 Reading8. Euler Walks and Hamilton WalksIntroduction; Euler Walks; Hamilton Walks; Multigraphs; The Königsberg Bridge Problem; Exercises; Suggested ReadingAfterwordSolutions to Selected ExercisesIndexSpecial symbols