The Scattering Matrix of a Graph

  • Hirobumi Mizuno
  • Iwao Sato

Abstract

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.

Published
2008-07-28
Article Number
R96