Introduction To Graph Theory - Brossura

Brossura

ISBN 10: 0486678709 ISBN 13: 9780486678702

Casa editrice: Dover Publications, 2025

Riassunto

Un'escursione stimolante nella matematica pura rivolta a "matematicamente traumatizzati", ma molto divertente anche per gli hobbisti matematici e per i matematici seri. Questo libro guida il lettore dai grafici semplici ai grafici planari, alla formula di Eulero, ai grafici platonici, alla colorazione, al genere di un grafico, ai cammini di Eulero, ai cammini di Hamilton e altro ancora. Include esercizi. Edizione del 1976.

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Contenuti

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

Product Description

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.

Dettagli dell'edizione

• Editore: Dover Publications
• Data di pubblicazione: 2025
• Lingua: Inglese
• ISBN 10: 0486678709
• ISBN 13: 9780486678702
• Rilegatura: Copertina flessibile
• Numero edizione: 2
• Numero di pagine: 209
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile