  We give a new determinant expression for the characteristic polynomial of the
bond scattering matrix of a quantum graph G. Also, we give a decomposition
formula for the characteristic polynomial of the bond scattering matrix of a
regular covering of G. Furthermore, we define an L-function of G, and give a
determinant expression of it. As a corollary, we express the characteristic
polynomial of the bond scattering matrix of a regular covering of G by means of
its L-functions. As an application, we introduce three types of quantum graph
walks, and treat their relation.
