I was wondering how to relate the spectra of the Zig-Zag product of two graphs in term of the factors...someone can help me?

  • $\begingroup$ What is the definition of the Zig-Zag product? $\endgroup$ – Richard Stanley Sep 10 '16 at 13:43
  • $\begingroup$ @RichardStanley See the wikipedia article, or the actual article cited in my answer. $\endgroup$ – Igor Rivin Sep 10 '16 at 17:54

The spectral gap is analyzed in the foundational paper I don't know if you can say anything else.

Omer Reingold, Salil Vadhan, and Avi Wigderson, MR 1888797 Entropy waves, the zig-zag graph product, and new constant-degree expanders, Ann. of Math. (2) 155 (2002), no. 1, 157--187.

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