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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Expander graphs in pure and applied mathematics
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by Alexander Lubotzky PDF
Bull. Amer. Math. Soc. 49 (2012), 113-162 Request permission


Expander graphs are highly connected sparse finite graphs. They play an important role in computer science as basic building blocks for network constructions, error correcting codes, algorithms, and more. In recent years they have started to play an increasing role also in pure mathematics: number theory, group theory, geometry, and more. This expository article describes their constructions and various applications in pure and applied mathematics.
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Additional Information
  • Alexander Lubotzky
  • Affiliation: Einstein Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel
  • MR Author ID: 116480
  • Email:
  • Received by editor(s): May 12, 2011
  • Received by editor(s) in revised form: June 7, 2011
  • Published electronically: November 2, 2011
  • Additional Notes: This paper is based on notes prepared for the Colloquium Lectures at the Joint Annual Meeting of the American Mathematical Society (AMS) and the Mathematical Association of America (MAA), New Orleans, LA, January 6–9, 2011. The author is grateful to the AMS for the opportunity to present this material for a wide audience. He has benefited by responses and remarks which followed his lectures

  • Dedicated: Dedicated to the memory of Jonathan Rogawski
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Bull. Amer. Math. Soc. 49 (2012), 113-162
  • MSC (2010): Primary 01-02, 05C99
  • DOI:
  • MathSciNet review: 2869010