h-Restricted H-structure connectivity and h-restricted H-substructure connectivity of hypercube.

The connectivity of a network is an important indicator to its reliability and fault tolerability. Since the faulty elements in the network may have some special structures, two new kinds of conditional connectivity, called h-restricted H-structure connectivity and h-restricted H-substructure connectivity, are proposed as a generalization of conditional connectivity, where h ≥ 1 , and H is some special structure. In this paper, we establish both h-restricted H-structure connectivity and h-restricted H-substructure connectivity for the hypercube Q n , where the special structures are K 1 , K 1 , 1 , K 1 , 2 , respectively. [ABSTRACT FROM AUTHOR]