Ruy Fabila-Monroy ; Jesús Leaños ; Ana Laura Trujillo-Negrete - On the Connectivity of Token Graphs of Trees

dmtcs:7538 - Discrete Mathematics & Theoretical Computer Science, March 30, 2022, vol. 24, no. 1 - https://doi.org/10.46298/dmtcs.7538
On the Connectivity of Token Graphs of Trees

Authors: 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 $F_k(G)$.


Volume: vol. 24, no. 1
Section: Graph Theory
Published on: March 30, 2022
Accepted on: February 14, 2022
Submitted on: June 3, 2021
Keywords: Mathematics - Combinatorics,05C40, 05C76


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