Introduction to Graph Theory (reprint) - Rilegato

Chartrand, Gary; Zhang, Ping

Rilegato

ISBN 10: 0073204161 ISBN 13: 9780073204161

Casa editrice: McGraw-Hill Higher Education, 2004

Riassunto

Written by one of the leading authors in the field, this text provides a student-friendly approach to graph theory for undergraduates. Much care has been given to present the material at the most effective level for students taking a first course in graph theory. Gary Chartrand and Ping Zhang's lively and engaging style, historical emphasis, unique examples and clearly-written proof techniques make it a sound yet accessible text that stimulates interest in an evolving subject and exploration in its many applications.

This text is part of the Walter Rudin Student Series in Advanced Mathematics.

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Contenuti

1 Introduction

1.1 Graphs and Graph Models

1.2 Connected Graphs

1.3 Common Classes of Graphs

1.4 Multigraphs and Digraphs

2 Degrees

2.1 The Degree of a Vertex

2.2 Regular Graphs

2.3 Degree Sequences

2.4 Excursion: Graphs and Matrices

2.5 Exploration: Irregular Graphs

3 Isomorphic Graphs

3.1 The Definition of Isomorphism

3.2 Isomorphism as a Relation

3.3 Excursion: Graphs and Groups

3.4 Excursion: Reconstruction and Solvability

4 Trees

4.1 Bridges

4.2 Trees

4.3 The Minimum Spanning Tree Problem

4.4 Excursion: The Number of Spanning Trees

5 Connectivity

5.1 Cut-Vertices

5.2 Blocks

5.3 Connectivity

5.4 Menger's Theorem

5.5 Exploration: Geodetic Sets

6 Traversability

6.1 Eulerian Graphs

6.2 Hamiltonian Graphs

6.3 Exploration: Hamiltonian Walks and Numbers

6.4 Excursion: The Early Books of Graph Theory

7 Digraphs

7.1 Strong Digraphs

7.2 Tournaments

7.3 Excursion: Decision-Making

7.4 Exploration: Wine Bottle Problems

8 Matchings and Factorization

8.1 Matchings

8.2 Factorization

8.3 Decompositions and Graceful Labelings

8.4 Excursion: Instant Insanity

8.5 Excursion: The Petersen Graph

8.6 Exploration: -Labeling of Graphs

9 Planarity

9.1 Planar Graphs

9.2 Embedding Graphs on Surfaces

9.3 Excursion: Graph Minors

9.4 Exploration: Embedding Graphs in Graphs

10 Coloring

10.1 The Four Color Problem

10.2 Vertex Coloring

10.3 Edge Coloring

10.4 Excursion: The Heawood Map Coloring Theorem

10.5 Exploration: Local Coloring

11 Ramsey Numbers

11.1 The Ramsey Number of Graphs

11.2 Turan's Theorem

11.3 Exploration: Rainbow Ramsey Numbers

11.4 Excursion: Erdös Numbers

12 Distance

12.1 The Center of a Graph

12.2 Distant Vertices

12.3 Excursion: Locating Numbers

12.4 Excursion: Detour and Directed Distance

12.5 Exploration: Channel Assignment

12.6 Exploration: Distance Between Graphs

13 Domination

13.1 The Domination Number of a Graph

13.2 Exploration: Stratification

13.3 Exploration: Lights Out

13.4 Excursion: And Still It Grows More Colorful

Appendix 1 Sets and Logic

Appendix 2 Equivalence Relations and Functions

Appendix 3 Methods of Proof

Product Description

Book by Chartrand Gary Zhang Ping

Dettagli dell?edizione

• Editore: McGraw-Hill Higher Education
• Data di pubblicazione: 2004
• ISBN 10: 0073204161
• ISBN 13: 9780073204161
• Rilegatura: Copertina rigida
• Lingua: Inglese
• Numero di pagine: 484