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

$\begingroup$ What is the definition of the ZigZag product? $\endgroup$– Richard StanleySep 10, 2016 at 13:43

$\begingroup$ @RichardStanley See the wikipedia article, or the actual article cited in my answer. $\endgroup$– Igor RivinSep 10, 2016 at 17:54
1 Answer
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 zigzag graph product, and new constantdegree expanders, Ann. of Math. (2) 155 (2002), no. 1, 157187.