On the Algebraic Connectivity of Token Graphs and Graphs under Perturbations

X Song, C Dalfó, MA Fiol, S Zhang - arXiv preprint arXiv:2412.21021, 2024 - arxiv.org
Given a graph $ G=(V, E) $ on $ n $ vertices and an integer $ k $ between 1 and $ n-1$, the
$ k $-token graph $ F_k (G) $ has vertices representing the $ k $-subsets of $ V $, and two …