Let \({\mathcal {T}}=\{T_1,T_2,\ldots ,T_k\}\) be a set of \(k\geqslant 2\) 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, \({\mathcal {T}}\) is called a dual-CIST (resp. tri-CIST) provided \(k=2\) (resp. \(k=3\)). From an algorithmic point of view, the problem of finding a dual-CIST in a given graph is known to be NP-hard. For data transmission applications in reliable networks, the existence of a dual-CIST can provide a configuration of fault-tolerant routing called protection routing. The presence of a tri-CIST can enhance the dependability of transmission and carry out secure message distribution for confidentiality. Recently, the construction of a dual-CIST has been proposed in a shuffle-cube \(SQ_n\), which is an innovative hypercube-variant network that possesses both short diameter and connectivity advantages. This paper uses the CIST-partition technique to construct a tri-CIST of \(SQ_6\), and shows that the diameters of three CISTs are 22, 22, and 13. Then, by the hierarchical structure of \(SQ_n\), we propose a recursive algorithm for constructing a tri-CIST for high-dimensional shuffle-cubes. When \(n\geqslant 10\), the diameters of \(T_i\), \(i=1,2,3\), we constructed for \(SQ_n\) are as follows: \(2n+11\), \(2n+9\), and \(2n+1\).

设\({\mathcal {T}}=\{T_1,T_2,\ldots ,T_k\}\)是图G中的一组\(k\geqslant 2\)生成树。如果在任何两棵树中连接每对顶点x和y的路径除了x和y之外没有共同的顶点和边，则这k个生成树称为完全独立的生成树（简称 CIST）。特别是，\({\mathcal {T}}\)被称为对偶 CIST (resp. tri-CIST)，前提是\(k=2\) (resp. \(k=3\)）。从算法的角度来看，已知在给定图中找到对偶 CIST 的问题是 NP-hard。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。tri-CIST 的存在可以增强传输的可靠性并进行安全的消息分发以实现机密性。最近，在 shuffle-cube \(SQ_n\)中提出了对偶 CIST 的构建，这是一种创新的超立方变体网络，具有短直径和连通性优势。本文使用 CIST-partition 技术构建了\(SQ_6\)的 tri-CIST，并表明三个 CIST 的直径分别为 22、22 和 13。然后，通过\(SQ_n\)的层次结构，我们提出了一种递归算法，用于构造高维 shuffle-cubes 的 tri-CIST。当\(n\geqslant 10\) ， \(T_i\)，\(i=1,2,3\)的直径，我们为\(SQ_n\)构造如下：\(2n+11\)、\(2n+9\)和\(2n+1\)。