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 $D_{k,n}$, 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 $\kappa (D_{k,n};S_m)$ and ${\kappa }^s(D_{k,n};S_m)$ when $k\ge 2$, $n\ge 4$ and $1\le m\le n+k-2$. Furthermore, we obtain both $\kappa (D_{k,n};S_{23})$ and ${\kappa }^s(D_{k,n};S_{23})$ for $k\ge 8$ and $n\ge 8$.