Let G = (V(G), E(G)) be a graph. A set S ⊆ E(G) is an edge k-cut in G if the graph G − S = (V(G), E(G) \ S) has at least k connected components. The generalized k-edge connectivity of a graph G, ...

A set of vertices S of a connected graph G is a nonseparating independent set if S is independent and G–S is connected. The nsis number 𝒵(G) is the maximum cardinality of a nonseparating independent ...