Treffer: The h-Faulty-Block Connectivity of n-Dimensional Locally Twisted Cube.

The connectivity of a network is an important indicator for assessing its reliability and fault-tolerability. In this paper, we study a novel measure, which is h -faulty-block connectivity. Given a connected graph G and a non-negative integer h , let C ⊂ V (G) and G [ C ] be connected subgraphs. Then, C is called an h -faulty-block of G if G − C disconnects G , and every remaining component of G − C has at least h + 1 nodes. The minimum cardinality over all h -faulty-blocks of G is called h -faulty-block connectivity of G , denoted by F B k h (G). In this paper, we focus on the locally twisted cube L T Q n . We study the { 0 , 1 , 2 } -faulty-block connectivity of L T Q n and show that F B k 0 (L T Q n) = 2 n − 1 for n ≥ 5 , F B k 1 (L T Q n) = 3 n − 4 for n ≥ 5 , and F B k 2 (L T Q n) = 4 n − 7 for n ≥ 7. [ABSTRACT FROM AUTHOR]

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