\magnification=1200
\hsize=4in
\overfullrule=0pt
\input amssym
%\def\frac#1 #2 {{#1\over #2}}
\def\emph#1{{\it #1}}
\def\em{\it}
\nopagenumbers
\noindent
%
%
{\bf Hirobumi Mizuno and Iwao Sato }
%
%
\medskip
\noindent
%
%
{\bf The Scattering Matrix of a Graph}
%
%
\vskip 5mm
\noindent
%
%
%
%
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.



\bye

.
