Introduction to Graph Theory (Reprint)

Chartrand, Gary; Zhang, Ping; Chartrand Gary

ISBN 10: 0073204161 / ISBN 13: 9780073204161

Editore: McGraw-Hill Science/Engineering/Math, 2004

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Titolo: Introduction to Graph Theory (Reprint)

Casa editrice: McGraw-Hill Science/Engineering/Math

Data di pubblicazione: 2004

Legatura: Hardcover

Condizione: Good

Condizione sovraccoperta: No Jacket

Descrizione articolo

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.

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