Description
This book discusses the origin of graph theory from its humble beginnings in recreational mathematics to its modern setting or modeling communication networks, as is evidenced by the World Wide Web graph used by many Internet search engines. The second edition of the book includes recent developments in the theory of signed adjacency matrices involving the proof of sensitivity conjecture and the theory of Ramanujan graphs. In addition, the book discusses topics such as Pick’s theorem on areas of lattice polygons and Graham–Pollak’s work on addressing of graphs. The concept of graph is fundamental in mathematics and engineering, as it conveniently encodes diverse relations and facilitates combinatorial analysis of many theoretical and practical problems. The text is ideal for a one-semester course at the advanced undergraduate level or beginning graduate level.
Table of Contents
Chapter 1. Basic Graph Theory.- Chapter 2. Basic Counting.- Chapter 3. The Principle of Inclusion and Exclusion.- Chapter 4. Graphs and Matrices.- Chapter 5. Trees.- Chapter 6. M¨obius Inversion and Graph Colouring.- Chapter 7. Enumeration under Group Action.- Chapter 8. Matching Theory.- Chapter 9. Block Designs.- Chapter 10. Planar Graphs.- Chapter 11. Edges and Cycles.- Chapter 12. Expanders and Ramanujan Graphs.- Chapter 13. Hints.
