Structure connectivity of hypercubes

The connectivity of a graph is an important measurement for the fault-tolerance of the network. To provide more accurate measures for the fault-tolerance of networks than the connectivity, some generalizations of connectivity have been introduced. Let H be a connected subgraph of a graph G. A set F of a connected subgraphs of G is called a subgraph cut of G if G−F is either disconnected or trivial. If further, each member of F is isomorphic to H, then F is called an H-structure cut of G. The H-structure connectivity κ(G;H) of G is the minimum cardinality of an H-structure cut of G. In this paper we determine κ(Qn;H) or its upper bound where Qn is the n-dimensional hypercube with n≥4 and H is either Qm with m≤n−2 or even cycle Cl with l≤2n.