Explicit construction of Ramanujan bigraphs

Abstract

We construct explicitly an infinite family of Ramanujan graphs which are bipartite and biregular. Our construction starts with the Bruhat-Tits building of an inner form of $S{U}_3({\mathbb{Q}}_p)$. To make the graphs finite, we take successive quotients by infinitely many discrete co-compact subgroups of decreasing size.

10 pages