دانلود کتاب A First Course in Graph Theory

فهرست مطالب :

Content: Cover Page
Title Page
Copyright Page
Dedication
Contents
Preface
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 Problem4.4. 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: Powers and Edge Labelings
6. Traversability
6.1. Eulerian Graphs
6.2. Hamiltonian Graphs
6.3. Exploration: Hamiltonian Walks
6.4. Excursion: 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 Labelings8.4. Excursion: Instant Insanity
8.5. Excursion: The Petersen Graph
8.6. Exploration: Bi-Graceful 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 Graphs
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: Modular Coloring
11. Ramsey Numbers
11.1. The Ramsey Number of Graphs
11.2. Turan\'s Theorem
11.3. Exploration: Modified Ramsey Numbers. 11.4. Excursion: Erdős Numbers12. 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
Solutions and Hints for Odd-Numbered Exercises.