A First Course in Graph Theory – Gary Chartrand, Ping Zhang – 1st Edition

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: 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 Labelings
8.4. 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