2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/114280The 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.15 pagesCombinatorics05C50text