The Scattering Matrix of a Graph
Copyright policy )The Scattering Matrix of a Graph
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.
- Toyama College Japan
determinant of its Laplacian, bond scattering matrix of a graph, Graphs and linear algebra (matrices, eigenvalues, etc.), Smilansky formula, Determinants, permanents, traces, other special matrix functions, Bass method
determinant of its Laplacian, bond scattering matrix of a graph, Graphs and linear algebra (matrices, eigenvalues, etc.), Smilansky formula, Determinants, permanents, traces, other special matrix functions, Bass method
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