A $k^{*}$-container of a graph G is a set of k disjoint paths between any pair of nodes whose union covers all nodes of G. The spanning connectivity of G, ${\kappa }^{*}\left(G\right)$, is the largest k, such that there exists a $j^{*}$-container between any pair of nodes of G for all $1\le j\le k$. If ${\kappa }^{*}\left(G\right)=\kappa \left(G\right)$, then G is super spanning connected. Spanning connectivity is an important property to measure the fault tolerance of an interconnection network. The divide-and-swap cube $DS{C}_n$ is a newly proposed hypercube variant, which reduces the network cost from $O\left(n^2\right)$ to $O\left(n{log}_{2}n\right)$ compared with the hypercube and other hypercube variants. The folded divide-and-swap cube $FDS{C}_n$ is proposed based on $DS{C}_n$ to reduce the diameter of $DS{C}_n$. Both $DS{C}_n$ and $FDS{C}_n$ possess many better properties than hypercubes. In this paper, we investigate the super spanning connectivity of $FDS{C}_n$ where $n=2^d$ and $d\ge 1$. We show that ${\kappa }^{*}\left(FDS{C}_n\right)=\kappa \left(FDS{C}_n\right)=d+2$, which means there exists an m-DPC(node-disjoint path cover) between any pair of nodes in $FDS{C}_n$ for all $1\le m\le d+2$.

The hypercube $Q_n$ is one of the most popular interconnection networks with high symmetry. To reduce the diameter of $Q_n$, many variants of $Q_n$ have been proposed, such as the n-dimensional locally twisted cube $LT{Q}_n$. To further optimize the diameter of $LT{Q}_n$, the n-dimensional folded locally twisted cube $FLT{Q}_n$ is proposed, which is built based on $LT{Q}_n$ by adding $2^{n-1}$ complementary edges. Connectivity is an important indicator to measure the fault tolerance and reliability of a network. However, the connectivity has an obvious shortcoming, in that it assumes all the adjacent vertices of a vertex will fail at the same time. Super-connectivity is a more refined index to judge the fault tolerance of a network, which ensures that each vertex has at least one neighbor. In this paper, we show that the super-connectivity ${\kappa }^{\left(1\right)}\left(FLT{Q}_n\right)=2n$ for any integer $n\ge 6$, which is about twice $\kappa \left(FLT{Q}_n\right)$.

BCube is one of the main data center networks because it has many attractive features. In practical applications, the failure of components or physical connections is inevitable. In data center networks in particular, switch failures are unavoidable. Fault-tolerance capability is one main aspect to measure the performance of data center networks. Connectivity, fault tolerance Hamiltonian connectivity, and fault tolerance Hamiltonicity are important parameters that assess the fault tolerance of networks. In general, the distribution of fault elements is scattered, and it is necessary to consider the distribution of fault elements in different dimensions. We research the fault tolerance of BCube when considering faulty switches and faulty links/edges that distribute in different dimensions. We also investigate the connectivity, fault tolerance Hamiltonian connectivity, and Hamiltonicity. This study better evaluates the fault-tolerant performance of data center networks.

The project-based teaching helps to stimulate students' enthusiasm for learning and to improve their ability to solve practical problems. To a certain extent, the quality of the case database affects the quality of project-based teaching. This paper proposes a case database generation method based on code automation technology and implements a code automatic generation tool to complete case code reconstruction, which could ensure completing the construction of the case database quickly and with high quality.