Generalized edge-connectivity of (n, k)-star graphs

An edge subset B is h-super edge-cut of a connected graph G if G - B is disconnected, moreover every vertex has at least h neighbors in G - B. Minimum |B| of G is h-super edge-connectivity of G, denoted by λ_s^(H) (G). In this paper, we determine λ_s^(H)(S_{n, k}) for 0 ≤ h ≤ n - k, where S_{n, k} de-notes (n, k)-star graphs, so that we can get traditional edge-connectivity λ (S_{n, k}) and λ_s(S_{n, k}) and get edge-connectivity of n-star graphs S_n who is isomorphic to S_{n, n-1}. In fact, the conclusions of generalized edge-connectivity in the known graphs are few, so this work is very valuable.