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arXiv · 2403.20148

A general method to find the spectrum and eigenspaces of the $k$-token of a cycle, and 2-token through continuous fractions

M. A. Reyes·C. Dalfó·M. A. Fiol·A. Messegué
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Abstract

The $k$-token graph $F_k(G)$ of a graph $G$ is the graph whose vertices are the $k$-subsets of vertices from $G$, two of which being adjacent whenever their symmetric difference is a pair of adjacent vertices in $G$. In this paper, we propose a general method to find the spectrum and eigenspaces of the $k$-token graph $F_k(C_n)$ of a cycle $C_n$. The method is based on the theory of lift graphs and the recently introduced theory of over-lifts. In the case of $k=2$, we use continuous fractions to derive the spectrum and eigenspaces of the 2-token graph of $C_n$.

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M. A. Reyes, C. Dalfó, M. A. Fiol, A. Messegué. 2024-03-29. A general method to find the spectrum and eigenspaces of the $k$-token of a cycle, and 2-token through continuous fractions. https://arxiv.org/abs/2403.20148

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