An expander (?) graph

Here is Theorem 4.4.2 in Lubotzky's lovely book "Discrete groups, expanding graphs and invariant measures". On the projective line over $\mathbb{F}_p$, connect $z$ to $z\pm 1$ and to $-\frac{1}{z}$; this is a family of 3-regular expander graphs. The proof is indeed based on Selberg's 3/16-theorem.

Here is one secondary reference:

Salil Vadhan, Lecture Notes, 2009. Chapter 4: Expander Graphs. p.62. (PDF download link)

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