Token graphs of Cayley graphs as lifts

Fuente: arXiv
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Auteurs principaux: Dalfó, C., Fiol, M. A., Pavlíková, S., Širáň, J.
Format: Preprint
Publié: 2024
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author Dalfó, C.
Fiol, M. A.
Pavlíková, S.
Širáň, J.
author_facet Dalfó, C.
Fiol, M. A.
Pavlíková, S.
Širáň, J.
contents This paper describes a general method for representing $k$-token graphs of Cayley graphs as lifts of voltage graphs. This allows us to construct line graphs of circulant graphs and Johnson graphs as lift graphs on cyclic groups. As an application of the method, we derive the spectra of the considered token graphs. This method can also be applied to dealing with other matrices, such as the Laplacian or the signless Laplacian, and to construct token digraphs of Cayley digraphs.
format Preprint
id arxiv_https___arxiv_org_abs_2404_02122
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Token graphs of Cayley graphs as lifts
Dalfó, C.
Fiol, M. A.
Pavlíková, S.
Širáň, J.
Combinatorics
This paper describes a general method for representing $k$-token graphs of Cayley graphs as lifts of voltage graphs. This allows us to construct line graphs of circulant graphs and Johnson graphs as lift graphs on cyclic groups. As an application of the method, we derive the spectra of the considered token graphs. This method can also be applied to dealing with other matrices, such as the Laplacian or the signless Laplacian, and to construct token digraphs of Cayley digraphs.
title Token graphs of Cayley graphs as lifts
topic Combinatorics
url https://arxiv.org/abs/2404.02122