Generalized fault-tolerance for enhanced hypercubes.

Fault-tolerance is an important indicator to measure the stability of the interconnection network. The connectivity can reflect the reliability of a network. The g -extra connectivity κ g (G) of a network G is a generalization of the connectivity. The enhanced hypercube Q n , k is an important variant of hypercube Q n which has been received many attentions in recent years. The g -extra connectivity of the enhanced hypercube was investigated for some special g and k in the literature. We fill the gap of k and determine κ g (Q n , k) for the remaining cases of k when g ≤ 3. In summary, we show that κ g (Q n , 3) = (g + 1) n − 4 (g − 1) and κ g (Q n , 4) = (g + 1) n − g (g − 1) where n ≥ 8 and 1 ≤ g ≤ 3. [ABSTRACT FROM AUTHOR]