  In this paper, we find computational formulae for generalized characteristic
polynomials of graph bundles. We show that the number of spanning trees in a
graph is the partial derivative (at (0,1)) of the generalized characteristic
polynomial of the graph. Since the reciprocal of the Bartholdi zeta function of
a graph can be derived from the generalized characteristic polynomial of a
graph, consequently, the Bartholdi zeta function of a graph bundle can be
computed by using our computational formulae.
