Graphs and digraphs treated here are finite and simple. Let G be a connected graph and D the symmetric digraph corresponding to G. A path P of length n in D(G) is a sequence P=(v0 , v1 , ..., vn&1 ,â€¦ (More)

We define a weighted zeta function of a digraph and a weighted L-function of a symmetric digraph, and give determinant expressions of them. Furthermore, we give a decomposition formula for theâ€¦ (More)

Recently, Smilansky expressed the determinant of the bond scattering matrix of a graph by means of the determinant of its Laplacian. We present another proof for this Smilanskyâ€™s formula by usingâ€¦ (More)

We give the (Ahumada type) Selberg trace formula for a semiregular bipartite graph G: Furthermore, we discuss the distribution on arguments of poles of zeta functions of semiregular bipartite graphs.â€¦ (More)

We give a decomposition formula for the Bartholdi zeta function of a graph G which is partitioned into some irregular coverings. As a corollary, we obtain a decomposition formula for the Bartholdiâ€¦ (More)