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arXiv · 2105.02677

The scattering matrix with respect to an Hermitian matrix of a graph

Takashi Komatsu·Norio Konno·Iwao Sato
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Abstract

Recently, Gnutzmann and Smilansky presented a formula for the bond scattering matrix of a graph with respect to a Hermitian matrix. We present another proof for this Gnutzmann and Smilansky's formula by a technique used in the zeta function of a graph. Furthermore, we generalize Gnutzmann and Smilansky's formula to a regular covering of a graph. Finally, we define an $L$-fuction of a graph, and present a determinant expression. As a corollary, we express the generalization of Gnutzmann and Smilansky's formula to a regular covering of a graph by using its $L$-functions.

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Takashi Komatsu, Norio Konno, Iwao Sato. 2021-05-05. The scattering matrix with respect to an Hermitian matrix of a graph. https://arxiv.org/abs/2105.02677

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