Ramanujan graphs and digraphs

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

Ramanujan graphs have fascinating properties and history. In this paper we explore a parallel notion of Ramanujan digraphs, collecting relevant results from old and recent papers, and proving some new ones. Almost-normal Ramanujan digraphs are shown to be of special interest, as they are extreme in the sense of an Alon-Boppana theorem, and they have remarkable combinatorial features, such as small diameter, Chernoff bound for sampling, optimal covering time and sharp cutoff. Other topics explored are the connection to Cayley graphs and digraphs, the spectral radius of universal covers, Alon's conjecture for random digraphs, and explicit constructions of almost-normal Ramanujan digraphs.
Original languageEnglish
Title of host publicationAnalysis and geometry on graphs and manifolds
Subtitle of host publicationSelected papers of the conference, University of Potsdam, Potsdam, Germany, July 31 -- August 4, 2017
PublisherCambridge University Press
Chapter13
Pages344-367
Number of pages24
ISBN (Print)978-1-108-71318-4; 978-1-108-61525-9
DOIs
StatePublished - 2020

Publication series

NameLondon Mathematical Society Lecture Note Series
PublisherCambridge University Press
Volume461

Keywords

  • Alon-Boppana theorem
  • Cayley graphs
  • Directed graphs
  • Expanders
  • Ramanujan

Fingerprint

Dive into the research topics of 'Ramanujan graphs and digraphs'. Together they form a unique fingerprint.

Cite this