Geodesic
The scattering matrix of a graph
The electronic journal of combinatorics, Tome 15 (2008)

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Zbl EuDML
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.
DOI : 10.37236/820
Classification : 05C50, 15A15
Mots-clés : bond scattering matrix of a graph, determinant of its Laplacian, Smilansky formula, Bass method 
Hirobumi Mizuno; Iwao Sato. The scattering matrix of a graph. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/820
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     author = {Hirobumi Mizuno and Iwao Sato},
     title = {The scattering matrix of a graph},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/820},
     zbl = {1163.05326},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/820/}
}
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