If two graphs and their Galois covers have the same Ihara zeta function, what can we say about the base graphs?

Question

I know that the Ihara zeta function being the same for two graphs does not necessitate an isomorphism between the graphs, but say instead the zeta functions were the same and the zeta functions of their Galois covers were the same. What could we say then? What if the same follows for the intermediate covers?