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 language | English |
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Title of host publication | Analysis and Geometry on Graphs and Manifolds |
Publisher | Cambridge University Press |
Pages | 344-367 |
Number of pages | 24 |
ISBN (Electronic) | 9781108615259 |
ISBN (Print) | 9781108713184 |
DOIs | |
State | Published - 1 Jan 2020 |
Externally published | Yes |
Keywords
- Alon-Boppana
- Cayley graphs
- Directed graphs
- Expanders
- Ramanujan
All Science Journal Classification (ASJC) codes
- General Mathematics