The scattering matrix with respect to an Hermitian matrix of a graph
Combinatorics
2021-05-07 v1
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 -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 -functions.
Keywords
Cite
@article{arxiv.2105.02677,
title = {The scattering matrix with respect to an Hermitian matrix of a graph},
author = {Takashi Komatsu and Norio Konno and Iwao Sato},
journal= {arXiv preprint arXiv:2105.02677},
year = {2021}
}
Comments
21 pages. arXiv admin note: substantial text overlap with arXiv:1211.4719