We investigate the Ihara zeta functions of finite Schreier graphs $\Gamma_n$ of the Basilica group. We show that $\Gamma_{ 1+n}$ is $2$ sheeted unramified normal covering of $\Gamma_n, ~\forall~ n \geq 1$ with Galois group $\displaystyle \frac{ \mathbb{ Z}}{ 2\mathbb{ Z}}.$ In fact, for any $n > 1, r \geq 1$ the graph $\Gamma_{ n+r}$ is $2^n$ sheeted unramified, non normal covering of $\Gamma_r.$ In order to do this we give the definition of the $generalized$ $replacement$ $product$ of Schreier graphs. We also show the corresponding results in zig zag product of Schreier graphs $\Gamma_n$ with a $4$ cycle.
Categories: math.GR