On Ramanujan bigraphs and general Ramanujan graphs

Shai Evra; Brooke Feigon; Kathrin Maurischat; Ori Parzanchevski

doi:10.5802/crmath.819

On Ramanujan bigraphs and general Ramanujan graphs

Shai Evra
, Brooke Feigon
, Kathrin Maurischat
, Ori Parzanchevski

Einstein Institute of Mathematics

Research output: Contribution to journal › Review article › peer-review

Abstract

In this paper, we give an overview of new results that define and explicitly construct Ramanujan Cayley biregular bipartite graphs. We also study the extremal combinatorial properties of these graphs. This parallels the work of Lubotzky, Phillips and Sarnak on regular Ramanujan Cayley graphs, with several interesting differences. Furthermore, this work also proposes a stronger definition of Ramanujan graphs than has been used in the past, which opens the door to future studies.

Original language	English
Pages (from-to)	71-78
Number of pages	8
Journal	Comptes Rendus Mathematique
Volume	364
DOIs	https://doi.org/10.5802/crmath.819
State	Published - 2026

Bibliographical note

Publisher Copyright:
© 2026, Academie des sciences. All rights reserved.

Keywords

Cayley bigraphs
Ramanujan conjecture
Ramanujan graphs
automorphic representations of U(3)
non-backtracking spectrum
pseudorandomness
simply-transitive lattices

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10.5802/crmath.819

Cite this

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KW - Ramanujan graphs

KW - automorphic representations of U(3)

KW - non-backtracking spectrum

KW - pseudorandomness

KW - simply-transitive lattices

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On Ramanujan bigraphs and general Ramanujan graphs

Abstract

Bibliographical note

Keywords

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