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 k(G; H) of G is the minimum cardinality of an H-structure cut of G. In this paper we determine k(Q(n); H) or its upper bound where Q(n) is the n-dimensional hypercube with n >= 4 and H is either Q(m) with m <= n - 2 or even cycle C-l with l <= 2(n) (C) 2018 Kalasalingam University. Publishing Services by Elsevier B.Y.