L-functions of regular coverings of graphs

Let π1 : K → H, π2 : H → G and π2π1 : K → G be three finite regular coverings of graphs, and let σ be a representation of the covering transformation group of π1. We show that the L-function of G associated to the representation of the covering transformation group of π2π1 induced from σ is equal to that of H associated to σ by means of ordinary voltage assignments.