Elementary Number Theory, Group Theory and Ramanujan Graphs

A self-contained treatment of expander graphs which are important in computer science, engineering and mathematics.

Giuliana Davidoff (Author), Peter Sarnak (Author), Alain Valette (Author)

9780521824262, Cambridge University Press

Hardback, published 27 January 2003

156 pages
22.9 x 15.2 x 1.3 cm, 0.4 kg

'A light touch and the inclusion of some unexpected results make the book a pleasure to read.' Mathematika

This text is a self contained treatment of expander graphs and in particular their explicit construction. Expander graphs are both highly connected but sparse, and besides their interest within combinatorics and graph theory, they also find various applications in computer science and engineering. The reader needs only a background in elementary algebra, analysis and combinatorics; the authors supply the necessary background material from graph theory, number theory, group theory and representation theory. The text can therefore be used as a brief introduction to these subjects as well as an illustration of how such topics are synthesised in modern mathematics.

An overview
1. Graph theory
2. Number theory
3. PSL2(q)
4. The graphs Xp,q
Appendix A. 4-regular graphs with large girth
Index
Bibliography.

Subject Areas: Combinatorics & graph theory [PBV], Number theory [PBH], Groups & group theory [PBG]