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{\bf Hirobumi Mizuno and Iwao Sato }
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{\bf The Scattering Matrix of a Graph}
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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 Smilansky's formula by using some
weighted zeta function of a graph.  Furthermore, we reprove a weighted
version of Smilansky's formula by Bass' method used in the determinant
expression for the Ihara zeta function of a graph.



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