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 two-dimensional torus, and present its explicit formula.
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We would like to thank the referees very much for many useful comments and improvement.
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Komatsu, T., Konno, N. & Sato, I. Vertex-Face/Zeta correspondence. J Algebr Comb 56, 527–545 (2022). https://doi.org/10.1007/s10801-022-01122-5
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DOI: https://doi.org/10.1007/s10801-022-01122-5