分层立方网络的条件容错性
On conditional fault tolerance of hierarchical cubic networks
摘要：
本文考虑了层次立方体网络$HCN_n$的条件容错性，$h$ -超连通性$κ^{h}$和$h$ -超边连通性$λ^{h}$，并给出了任意具有$0\leq h\leq n-1$的$h$的$κ^h(HCN_n)=λ^h(HCN_n)=2^h(n+1-h)$.结果表明，要使$HCN_n$不连通，且不存在度小于$h$的点，至少要去掉$2^h(n+1-h)$点或边，推广了一些已知结果.
英文摘要：
This paper considers the conditional fault tolerance, $h$-super connectivity $κ^{h}$ and $h$-super edge-connectivity $λ^{h}$ of the hierarchical cubic network $HCN_n$, an attractive alternative network to the hypercube, and shows $κ^h(HCN_n)=λ^h(HCN_n)=2^h(n+1-h)$ for any $h$ with $0\leq h\leq n-1$. The results imply that at least $2^h(n+1-h)$ vertices or edges have to be removed from $HCN_n$ to make it disconnected with no vertices of degree less than $h$, and generalize some known results.
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