The k-token graph T k (G) is the graph whose vertices are the k-subsets of vertices of a graph G, with two vertices of T k (G) adjacent if their symmetric difference is an edge of G. We explore when T k (G) is a well-covered graph, that is, when all of its maximal independent sets have the same cardinality. For bipartite graphs G, we classify when T k (G) is well-covered. For an arbitrary graph G, we show that if T 2 (G) is well-covered, then the girth of G is at most four. We include upper and lower bounds on the independence number of T k (G), and provide some families of well-covered token graphs.

The k-token graph T k (G) is the graph whose vertices are the k-subsets of vertices of a graph G, with two vertices of T k (G) adjacent if their symmetric difference is an edge of G. We explore when T k (G) is a well-covered graph, that is, when all of its maximal independent sets have the same cardinality. For bipartite graphs G, we classify when T k (G) is well-covered. For an arbitrary graph G, we show that if T2(G) is wellcovered, then the girth of G is at most four. We include upper and lower bounds on the independence number of T k (G), and provide some families of well-covered token graphs.