A First Course in Graph Theory and Combinatorics

Contents: 1. Basic notions of graph theory. 2. Recurrence relations. 3. The principle of inclusion and exclusion. 4. Matrices and graphs. 5. Trees. 6. Mobius inversion and graph colouring. 7. Enumeration under group action. 8. Matching theory. 9. Block designs. 10. Planar graphs. 11. Edges and cycles. 12. Regular graphs. 13. Hints. Bibliography. Index. "The concept of a graph is fundamental in mathematics since it conveniently encodes diverse relations and facilitates combinatorial analysis of many complicated counting problems. In this book, we have traced the origins of graph theory from its humble beginnings in recreational mathematics to its modern setting for modeling communication networks, as is evidenced by the World Wide Web graph used by many internet search engines. This book is an introduction to graph theory and combinatorial analysis. It is based on courses given by the second author at Queen's University at Kingston, Ontario, Canada between 2002 and 2008. The courses were aimed at students in the final year of their undergraduate program. This text is very suitable for a first course on this topic.".…