On Ramanujan bigraphs and general Ramanujan graphs

Comptes Rendus Mathématique, vol. 364, pp. 71–78

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.

Authors 4

1. Shai Evra

   Hebrew University of Jerusalem

   Affiliation as printed

   Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Israel

2. Brooke Feigon

   City College of New York · City University of New York

   Affiliation as printed

   Department of Mathematics, The City College of New York, CUNY, New York, NY 10031, USA

3. Kathrin Maurischat Aachen Lehrstuhl für Algebra und Darstellungstheorie

   RWTH Aachen University

   Affiliation as printed

   Lehrstuhl für Algebra und Darstellungstheorie, RWTH Aachen University, 52062 Aachen, Germany

4. Ori Parzanchevski

   Hebrew University of Jerusalem

   Affiliation as printed

   Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Israel