The <i>h</i> -Faulty-Block Connectivity of <i>n</i> -Dimensional Balanced Hypercube

The connectivity of a network is an important indicator for assessing its reliability and fault-tolerability. In this paper, we study a novel measurement, which is h-faulty-block connectivity. Let G be a connected graph, [Formula: see text] and [Formula: see text] be a connected subgraph. Then, C is called an h-fault-block of G if [Formula: see text] is disconnected, and every component of [Formula: see text] has at least [Formula: see text] nodes with a non-negative integer h. The minimum cardinality over all h-fault-blocks of G is called h-fault-block connectivity of G, denoted by [Formula: see text]. In this paper, we determine [Formula: see text] for n-dimensional balanced hypercube [Formula: see text], a variation of the hypercube. We prove that [Formula: see text] for [Formula: see text], [Formula: see text] for [Formula: see text], and [Formula: see text] for [Formula: see text].