Constructing edge-disjoint spanning trees in several cube-based networks with applications to edge fault-tolerant communication

If a set of spanning trees of a graph do not share any edge with each other, they are called edge-disjoint spanning trees (for short EDSTs), which have widespread practical applications, such as fault-tolerant broadcasting, the distributed algorithms against Man-in-the-Middle attacks, the efficient collective communication algorithms, and so on. Crossed cubes, folded cubes, and folded crossed cubes, as three important variations of hypercubes, are optimized in terms of communication efficiency and fault tolerance of networks. In this paper, we propose a recursive algorithm to construct the maximum number of EDSTs in the three kinds of cube-based networks. Additionally, relying on the resulting EDSTs, the performance of one-to-one communication and one-to-all communication with edge failures are evaluated by simulation results in folded crossed cubes.