The Edge-Connectivity of Token Graphs

Let G be a simple graph of order $$n\ge 2$$ and let $$k\in \{1,\ldots ,n-1\}$$ . The k-token $$F_k(G)$$ is the whose vertices are k-subsets V(G), where two adjacent in whenever their symmetric difference an edge G. In 2018 Leaños Trujillo-Negrete proved that if t-connected $$t\ge k$$ , then at least $$k(t-k+1)$$ -connected. this paper we show such lower bound remains true context edge-connectivity. Specifically, t-edge-connected -edge-connected. We also provide some families graphs attaining bound.