Vertex-Face/Zeta correspondence

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...

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Veröffentlicht in:Journal of algebraic combinatorics 2022-09, Vol.56 (2), p.527-545
Hauptverfasser: Komatsu, Takashi, Konno, Norio, Sato, Iwao
Format: Artikel
Sprache:eng
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Zusammenfassung: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 two-dimensional torus, and present its explicit formula.
ISSN:0925-9899
1572-9192
DOI:10.1007/s10801-022-01122-5