Treffer: The h-Faulty-Block Connectivity of n-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, C ⊂ V (G) and G [ C ] be a connected subgraph. Then, C is called an h-fault-block of G if G − C is disconnected, and every component of G − C has at least h + 1 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 F B k h (G). In this paper, we determine F B k h (B H n) for n-dimensional balanced hypercube B H n , a variation of the hypercube. We prove that F B k 0 (B H n) = 2 n + 1 for n ≥ 2 , F B k 1 (B H n) = 4 n − 2 for n ≥ 3 , and F B k 2 (B H n) = 6 n − 5 for n ≥ 4. [ABSTRACT FROM AUTHOR]