Characteristic polynomials of graph bundles having voltages in a dihedral group

In this paper, we compute the characteristic polynomial of a graph bundle when its voltages lie in a dihedral group, as the first attempt to compute the characteristic polynomial of a graph bundle (also, of a graph covering) having voltages in a nonabelian group. As a result, we compute the characteristic polynomial of a graph bundle having a circulant graph as a fibre. It is applied for the characteristic polynomials of a discrete torus and a discreteKlein bottle.