The Edge-Connectivity of Token Graphs

Let G be a simple graph of order n >= 2 and let k is an element of {1, ..., 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. In 2018 Leafios and Trujillo-Negrete proved that if G is t-connected and t >= k, then F-k(G) is at least k(t - k + 1)-connected. In this paper we show that such a lower bound remains true in the context of edge-connectivity. Specifically, we show that if G is t-edge-connected and t >= k, then F-k(G) is at least k(t - k + 1)-edge-connected. We also provide some families of graphs attaining this bound.