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[ACM Press the eighteenth annual ACM symposium - Berkeley, California, United States (1986.05.28-1986.05.30)] Proceedings of the eighteenth annual ACM symposium on Theory of computing - STOC '86 - Explicit expanders and the Ramanujan conjectures

✍ Scribed by Lubotzky, A; Phillips, R; Sarnak, P

Book ID
121280297
Publisher
ACM Press
Year
1986
Weight
284 KB
Category
Article
ISBN-13
9780897911931

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[ACM Press the eighteenth annual ACM sym
[ACM Press the eighteenth annual ACM symposium - Berkeley, California, United States (1986.05.28-1986.05.30)] Proceedings of the eighteenth annual ACM symposium on Theory of computing - STOC '86 - Explicit expanders and the Ramanujan conjectures
✍ Lubotzky, A; Phillips, R; Sarnak, P πŸ“‚ Article πŸ“… 1986 πŸ› ACM Press βš– 284 KB

1. Background. The aim of this note is to give an explicit construction of a rich family of k-regular (except for k Β° =k) of the adjacency matrix satisfy Ikjl < 2 k~-l. graphs for which all the eigenvalues kj This bound is optimal (see Proposition 2.1). We call such graphs Ramanujan graphs. These g