For any integers $m\ge 0$ and $n\ge 2,$ we use $D_{m,n}$ to denote the $m$-dimensional DCell with $n$-port switches. For a simple graph $G=(V,E),$ an edge subset $S\subset E\left(G\right)$ is said to be a ${\lambda }_k$-cut of $G,$ if $G-S$ is disconnected and each component of $G-S$ has at least $k$ vertices. The $k$-restricted edge-connectivity of $G,$ denoted by ${\lambda }_k\left(G\right),$ is the minimum cardinality of all ${\lambda }_k$-cuts of $G$. We prove that ${\lambda }_k\left(D_{m,n}\right)=k(m+n-k)$ for $m\ge n\ge 2$ and $2\le k\le n,$ ${\lambda }_k\left(D_{m,n}\right)=mn$ for $n>m\ge 2$ and $m\le k\le n$ and ${\lambda }_k\left(D_{m,n}\right)=k(m+n-k)$ for $n>m\ge 2$ and $2\le k<m$. We also characterize the structure of the minimum ${\lambda }_k$-cuts of $D_{m,n}$ in terms of the above conclusions.

对于任何整数 $米\ge 0$ 和 $ñ\ge 2，$ 我们用 $d_{米，ñ}$ 表示 $米$DCell具有 $ñ$端口开关。对于一个简单的图$G=（V，Ë），$ 边缘子集 $\mathrm{小号}\subset Ë（G）$ 据说是 ${\lambda }_{ķ}$-切 $G，$ 如果 $G-\mathrm{小号}$ 断开连接，并且 $G-\mathrm{小号}$ 至少有 $ķ$顶点。的$ķ$的有限边缘连接性 $G，$ 表示为 ${\lambda }_{ķ}（G），$ 是所有的最小基数 ${\lambda }_{ķ}$-削减 $G$。我们证明${\lambda }_{ķ}（d_{米，ñ}）=ķ（米+ñ-ķ）$ 对于 $米\ge ñ\ge 2$ 和 $2\le ķ\le ñ，$ ${\lambda }_{ķ}（d_{米，ñ}）=米ñ$ 对于 $ñ>米\ge 2$ 和 $米\le ķ\le ñ$ 和 ${\lambda }_{ķ}（d_{米，ñ}）=ķ（米+ñ-ķ）$ 对于 $ñ>米\ge 2$ 和 $2\le ķ<米$。我们还描述了最小值的结构${\lambda }_{ķ}$-削减 $d_{米，ñ}$ 根据以上结论。