Independence and matching numbers of some token graphs

Abstract

Let $G$ be a graph of order $n$ and let $k\in \{1,\dots ,n-1\}$. 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 $G$. We study the independence and matching numbers of $F_k(G)$. We present a tight lower bound for the matching number of $F_k(G)$ for the case in which $G$ has either a perfect matching or an almost perfect matching. Also, we estimate the independence number for bipartite $k$-token graphs, and determine the exact value for some graphs.

16 pages, 4 figures. Third version is a major revision. Some proofs were corrected or simplified. New references added

Cited by in corpus (3)

• The automorphism groups of some token graphs
• Independence numbers of some double vertex graphs and pair graphs
• Well-covered Token Graphs