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.

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Correspondence to Yair Glasner.

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

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AMS Subject Classification (2000):

  • 05Cxx
  • 05C25
  • 22E40