Elementary Number Theory, Group Theory and Ramanujan Graphs

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Cambridge University Press, Jan 20, 2003 - Mathematics - 144 pages
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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 from graph theory, number theory, group theory and representation theory. Thus the text can be used as a brief introduction to these subjects and their synthesis in modern mathematics.
 

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Contents

Chapter 1 Graph Theory
8
Chapter 2 Number Theory
38
Chapter 3 PSLq
72
Chapter 4 The Graphs X
108
Appendix 4Regular Graphs with Large Girth
132
Bibliography
138
Index
143
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