Discrete Mathematics is one
of the fastest growing areas in mathematics today with an ever-increasing number of
courses in schools and universities. Graphs and Applications is based on a highly
successful Open University course and the authors have paid particular attention to the
presentation, clarity and arrangement of the material, making it ideally suited for
independent study and classroom use. An important part of learning graph theory is problem
solving; for this reason large numbers of examples, problems (with full solutions) and
exercises (without solutions) are included.
Accompanying the book is a
CD-ROM comprising a Graphs Database, containing all the simple unlabelled graphs with up
to seven vertices, and a Graphs Editor that enables students to construct and manipulate
graphs. Both the Database and Editor are simple to use and allow students to investigate
graphs with ease. Computing Notes and suggested activities are provided.
Contents
1. Introduction
2. Graphs
3. Eulerian and Hamiltonian
Graphs
4. Digraphs
5. Matrix Representations
6. Tree Structures
7. Counting Trees
8. Greedy Algorithms
9. Path Algorithms
10. Connectivity
11. Planarity
12. Vertex Colourings and
Decompositions
13. Edge Colourings and
Decompositions
14. Conclusion
Suggestions for Further
Reading
Appendix: Methods of Proof
Solutions to the Problems
Computer Notes
Index
444 pages