This comprehensive text offers undergraduates a remarkably student-friendly introduction to graph theory. Written by two of the field's most prominent experts, it takes an engaging approach that emphasizes graph theory's history. Unique examples and lucid proofs provide a sound yet accessible treatment that stimulates interest in an evolving subject and its many applications. Optional sections designated as "excursion" and "exploration" present interesting sidelights of graph theory and touch upon topics that allow students the opportunity to experiment and use their imaginations. Three appendixes review important facts about sets and logic, equivalence relations and functions, and the methods of proof. The text concludes with solutions or hints for odd-numbered exercises, in addition to references, indexes, and a list of symbols.

1. Introduction

2. Degrees

3. Isomorphic Group

4. Trees

5. Connectivity

6. Traversability

7. Digraphs

8. Matchings and Factorization

9. Planarity

10. Coloring Graphs

11. Ramsy Numbers

12. Distance

13. Domination

Appendix 1

Appendix 2

Appendix 3

Solutions and Hints for Odd-Numbered Exercises

References

Index of Names

Index of Mathematical Terms

List of Symbols