1. Vertex-Face/Zeta correspondence
- Author
-
Komatsu, Takashi, Konno, Norio, and Sato, Iwao
- Subjects
Mathematics - Combinatorics ,60F05, 05C10, 05C50, 15A15 - 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., Comment: 14 pages. arXiv admin note: text overlap with arXiv:2103.12971, arXiv:2011.14162
- Published
- 2021