Fault-tolerance of ðn; kÞ-star networks

a b s t r a c t This paper considers a refined measure j ðhÞ s for the fault-tolerance of a network and, for the generalized star network S n;k , determines j ðhÞ s ðS n;k Þ ¼ n þ hðk À 2Þ À 1 for 2 6 k 6 n À 1 and 0 6 h 6 n À k, which implies that at least n þ hðk À 2Þ À 1 vertices of S n;k have to be removed to get a disconnected graph without vertices of degree less than h. This work generalizes some known results. When the ðn; kÞ-star graph is used to model the topological structure of a large-scale parallel processing system, this result can provide a more accurate measure for the fault tolerance of the system