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{\bf Iwao Sato }
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{\bf Weighted Zeta Functions of Graph Coverings}
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We present a decomposition formula for the weighted zeta function of
an irregular covering of a graph by its weighted $L$-functions.
Moreover, we give a factorization of the weighted zeta function of an
(irregular or regular) covering of a graph by equivalence classes of
prime, reduced cycles of the base graph. As an application, we
discuss the structure of balanced coverings of signed graphs.
\bye