On the Connectivity of Token Graphs of TreesArticle
Authors: Ruy Fabila-Monroy ; Jesús Leaños ; Ana Laura Trujillo-Negrete
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Ruy Fabila-Monroy;Jesús Leaños;Ana Laura Trujillo-Negrete
Let $k$ and $n$ be integers such that $1\leq k \leq n-1$, and let $G$ be a
simple graph of order $n$. The $k$-token graph $F_k(G)$ of $G$ is the graph
whose vertices are the $k$-subsets of $V(G)$, where two vertices are adjacent
in $F_k(G)$ whenever their symmetric difference is an edge of $G$. In this
paper we show that if $G$ is a tree, then the connectivity of $F_k(G)$ is equal
to the minimum degree of $F_k(G)$.
Christophe Ndjatchi;Joel Alejandro Escareño Fernández;L. M. Ríos-Castro;Teodoro Ibarra-Pérez;Hans Christian Correa-Aguado;et al., 2024, On the packing number of $ 3 $-token graph of the path graph $ P_n $, AIMS Mathematics, 9, 5, pp. 11644-11659, 10.3934/math.2024571, https://doi.org/10.3934/math.2024571.