（n，k）-星图边容错的广义测度
Generalized Measures of Edge Fault Tolerance in (n,k)-star Graphs
摘要：
本文考虑$(n,k)$中的一种广义容错测度$λ_s^{(h)}$--$2\leqslant k \leqslant n-1$和$0\leqslant h \leqslant n-k$的星图$S_{n,k}$，并确定了$λ_s^{(h)}(S_{n,k})=\min\{(n-h-1)(h+1), (n-k+1)(k-1)\}$，这意味着要得到一个不包含度小于$h$的点的不连通图，至少要去掉$S_{n,k}$的$\min\{(n-k+1)(k-1),(n-h-1)(h+1)\}$条边.这一结果表明，$(n,k)$ -星图是强大的，当它被用来建模的大规模并行处理系统的拓扑结构。
英文摘要：
This paper considers a kind of generalized measure $λ_s^{(h)}$ of fault tolerance in the $(n,k)$-star graph $S_{n,k}$ for $2\leqslant k \leqslant n-1$ and $0\leqslant h \leqslant n-k$, and determines $λ_s^{(h)}(S_{n,k})=\min\{(n-h-1)(h+1), (n-k+1)(k-1)\}$, which implies that at least $\min\{(n-k+1)(k-1),(n-h-1)(h+1)\}$ edges of $S_{n,k}$ have to remove to get a disconnected graph that contains no vertices of degree less than $h$. This result shows that the $(n,k)$-star graph is robust when it is used to model the topological structure of a large-scale parallel processing system.
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