High fault tolerance and reliability of multiprocessor systems, modeled by interconnection network, are of great significance to assess the flexibility and effectiveness of the systems. Connectivity is an important metric to evaluate the fault tolerance and reliability of interconnection networks. As classical connectivity is not suitable for such large scale systems, a novel and generalized connectivity, structure connectivity and substructure connectivity, has been proposed to measure the robustness of networks and has witnessed rich achievements. The divide-and-swap cube $DS{C}_n$ is an interesting variant of hypercube that has nice hierarchical properties. In this paper, we mainly investigate $\mathcal{H}$-structure-connectivity, denoted by $\kappa (DS{C}_n;\mathcal{H})$, and $\mathcal{H}$-substructure-connectivity, denoted by ${\kappa }^s(DS{C}_n;\mathcal{H})$, for $\mathcal{H}\in \{K_1,K_{1,1},K_{1,m}(2\le m\le d+1),C_4\}$, respectively. In detail, we show that $\kappa (DS{C}_n;K_1)={\kappa }^s(DS{C}_n;K_1)=d+1$ for $n\ge 2$, $\kappa (DS{C}_n;K_{1,1})={\kappa }^s(DS{C}_n;K_{1,1})=d+1$ for $n\ge 8$, $\kappa (DS{C}_n;K_{1,m})={\kappa }^s(DS{C}_n;K_{1,m})=\lfloor \frac{d}{2}\rfloor +1$ with $2\le m\le d+1$ for $n\ge 4$, $\kappa (DS{C}_n;C_4)=3+2(d-2)$ for $4\le n\le 8$, $\lfloor \frac{d}{2}\rfloor +1\le \kappa (DS{C}_n;C_4)\le d+1$ for $n\ge 16$ and ${\kappa }^s(DS{C}_n;C_4)=\lfloor \frac{d}{2}\rfloor +1$ for $n\ge 4$. Finally, we compare and analyze the ratios of structure (resp. substructure) connectivity to vertex degree of divide-and-swap cube with that of several well-known variants of hypercube.

以互连网络建模的多处理器系统的高容错性和可靠性对于评估系统的灵活性和有效性具有重要意义。连通性是评价互连网络容错性和可靠性的重要指标。由于经典连通性不适用于如此大规模的系统，因此提出了一种新颖的广义连通性、结构连通性和子结构连通性来衡量网络的鲁棒性，并取得了丰硕的成果。分而治之的立方体$D秒C_n$是超立方体的一个有趣的变体，具有很好的层次属性。在本文中，我们主要研究$\mathcal{H}$-结构-连通性，表示为 $\kappa (D秒C_n;\mathcal{H})$， 和 $\mathcal{H}$-子结构-连通性，表示为 ${\kappa }^{秒}(D秒C_n;\mathcal{H})$， 为了 $\mathcal{H}\in \{{钾}_1,{钾}_{1,1},{钾}_{1,米}(2\le 米\le d+1),C_4\}$， 分别。详细地，我们证明$\kappa (D秒C_n;{钾}_1)={\kappa }^{秒}(D秒C_n;{钾}_1)=d+1$ 为了 $n\ge 2$, $\kappa (D秒C_n;{钾}_{1,1})={\kappa }^{秒}(D秒C_n;{钾}_{1,1})=d+1$ 为了 $n\ge 8$, $\kappa (D秒C_n;{钾}_{1,米})={\kappa }^{秒}(D秒C_n;{钾}_{1,米})=\lfloor \frac{d}{2}\rfloor +1$ 和 $2\le 米\le d+1$ 为了 $n\ge 4$, $\kappa (D秒C_n;C_4)=3+2(d-2)$ 为了 $4\le n\le 8$, $\lfloor \frac{d}{2}\rfloor +1\le \kappa (D秒C_n;C_4)\le d+1$ 为了 $n\ge 16$ 和 ${\kappa }^{秒}(D秒C_n;C_4)=\lfloor \frac{d}{2}\rfloor +1$ 为了 $n\ge 4$. 最后，我们将结构（或子结构）连通性与分交换立方体的顶点度的比率与几个众所周知的超立方体变体的比率进行比较和分析。