  The Jacobian group of a graph is a finite abelian group through which we can
study the graph in an algebraic way. When the graph is a finite abelian
covering of another graph, the Jacobian group is equipped with the action of
the Galois group. In this paper, we study the Fitting ideal of the Jacobian
group as a module over the group ring. We also study the corresponding question
for infinite coverings. Additionally, this paper includes module-theoretic
approach to Iwasawa theory for graphs.
