Properties of the Generalized Zig-Zag Product of Graphs
  The operation of zig-zag products of graphs is the analogue of the semidirect product of groups. Using this observation, we present a categorical description of zig-zag products in order to generalize the construction for the category of simple graphs. Also, we examine the covering properties of zig-zag products and we utilize these results to estimate their spectral invariants in general. In addition, we provide specific spectral analysis for some such products. 
Samuel Cooper, Dominic Dotterrer, Stratos Prassidis