Structure connectivity and substructure connectivity of data center network

The structure connectivity kappa(G; H) and substructure connectivity kappa s(G; H) are important indicators to measure interconnection network's fault tolerance and reliability. The data center network, denoted by Dk,n, have been proposed for data centers as a server-centric interconnection network structure, which can support millions of servers with high network capacity by only using commodity switches. In this paper, we obtain kappa(Dk,n; Sm) and kappa s(Dk,n; Sm) when k >= 2, n >= 4 and 1 <= m <= n+ k - 2. Furthermore, we obtain both kappa(Dk,n; S23) and kappa s(Dk,n; S23) fork >= 8 and n >= 8.