Let ${𝒯}=\{T_1,T_2,\dots ,T_k\}$ be a set of $k\ge 2$ spanning trees in a graph $G$. The $k$ spanning trees are called completely independent spanning trees (CISTs for short) if the paths joining every pair of vertices $x$ and $y$ in any two trees have neither vertex nor edge in common except for $x$ and $y$. Particularly, ${𝒯}$ is called a dual-CIST provided $k=2$. For data transmission applications in reliable networks, the existence of a dual-CIST can provide a configuration of fault-tolerant routing called protection routing. This paper investigates the problem of constructing a dual-CIST in the $n$-dimensional hierarchical folded cubic network $HF{Q}_n$. The network is a two-level network using folded hypercube $F{Q}_n$ as clusters to reduce the diameter, hardware overhead and improve the fault tolerance ability. We propose a recursive algorithm to construct a dual-CIST of $HF{Q}_n$ in ${𝒪}(2^{2n})$ time for $n\ge 2$, where the time required is the same scale as the number of vertices of $HF{Q}_n$. Also, the diameter of each constructed CIST is $4n+1$.

让${𝒯}=\{{\mathrm{时间}}_1,{\mathrm{时间}}_2,\dots \dots ,{\mathrm{时间}}_k\}$是一组$k\ge 2$图中的生成树$G$。这$k$如果连接每对顶点的路径，则生成树称为完全独立生成树（简称 CIST）$X$和$y$任何两棵树都没有共同的顶点和边，除了$X$和$y$。特别，${𝒯}$被称为双 CIST 提供$k=2$。对于可靠网络中的数据传输应用，双CIST的存在可以提供一种称为保护路由的容错路由配置。本文研究了双CIST的构建问题。$n$维分层折叠立方网络$HF{问}_n$。该网络是使用折叠超立方体的两级网络$F{问}_n$由于集群直径减小，硬件开销增加，容错能力提高。我们提出了一种递归算法来构造一个双 CIST$HF{问}_n$在${𝒪}（2^{2n}）$的时间$n\ge 2$，其中所需的时间与顶点数量相同$HF{问}_n$。此外，每个构造的 CIST 的直径为$4n+1$。