Vertex-Face/Zeta correspondence
Combinatorics
2021-07-08 v1
Abstract
We present the characteristic polynomial for the transition matrix of a vertex-face walk on a graph, and obtain its spectra. Furthermore, we express the characteristic polynomial for the transition matrix of a vertex-face walk on the 2-dimensional torus by using its adjacency matrix, and obtain its spectra. As an application, we define a new walk-type zeta function with respect to the transition matrix of a vertex-face walk on the 2-dimensional torus, and present its explicit formula.
Keywords
Cite
@article{arxiv.2107.03300,
title = {Vertex-Face/Zeta correspondence},
author = {Takashi Komatsu and Norio Konno and Iwao Sato},
journal= {arXiv preprint arXiv:2107.03300},
year = {2021}
}
Comments
14 pages. arXiv admin note: text overlap with arXiv:2103.12971, arXiv:2011.14162