Abstract
We define a new weighted Ihara zeta function of a graph G, and present its determinant expression. We present a decomposition formula for the new weighted Ihara zeta function of a regular covering of G. Furthermore, we introduce a new weighted Ihara L-function of G, and give determinant expressions of it. As a corollary, we present a decomposition formula for the new weighted Ihara zeta function of a regular covering of G by its new weighted Ihara L-functions. As applications, we give new proofs for the results of Kempton on the spectrum of the transition probability matrices for non-backtracking random walks for regular graphs and semiregular bipartite graphs.
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