Ramanujan Graphs with Small Girth

We construct an infinite family of (q + 1)-regular Ramanujan graphs X n of girth 1. We also give covering maps X n+1X n such that the minimal common covering of all the X n ’s is the universal covering tree.

This is a preview of subscription content, access via your institution.

Author information



Corresponding author

Correspondence to Yair Glasner.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Glasner, Y. Ramanujan Graphs with Small Girth. Combinatorica 23, 487–502 (2003). https://doi.org/10.1007/s00493-003-0029-9

Download citation

AMS Subject Classification (2000):

  • 05Cxx
  • 05C25
  • 22E40