Ramanujan graphs

A. Lubotzky*, R. Phillips, P. Sarnak

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1079 Scopus citations

Abstract

A large family of explicit k-regular Cayley graphs X is presented. These graphs satisfy a number of extremal combinatorial properties. (i) For eigenvalues λ of X either λ=±k or |λ|≦2 √k-1. This property is optimal and leads to the best known explicit expander graphs. (ii) The girth of X is asymptotically ≧4/3 logk-1 |X| which gives larger girth than was previously known by explicit or non-explicit constructions.

Original languageEnglish
Pages (from-to)261-277
Number of pages17
JournalCombinatorica
Volume8
Issue number3
DOIs
StatePublished - Sep 1988

Keywords

  • AMS subject classification (1980): 05C35

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