Token graphs of Cayley graphs as lifts

2024/04/02 by C. Dalfó, M.A. Fiol, Dalfó, C. +5 · 1 citation
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems

paper · pdf · doi:10.48550/arxiv.2404.02122

openalex publication_date 2024/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

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.

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