Independent spanning trees on twisted cubes

Multiple independent spanning trees have applications to fault tolerance and data broadcasting in distributed networks. There are two versions of the n independent spanning trees conjecture. The vertex (edge) conjecture is that any n-connected (n-edge-connected) graph has n vertex-independent spanning trees (edge-independent spanning trees) rooted at an arbitrary vertex. Note that the vertex conjecture implies the edge conjecture. The vertex and edge conjectures have been confirmed only for n-connected graphs with n <= 4, and they are still open for arbitrary n-connected graph when n >= 5. In this paper, we confirm the vertex conjecture (and hence also the edge conjecture) for the n-dimensional twisted cube TQ(n) by providing an O(N log N) algorithm to construct n vertex-independent spanning trees rooted at any vertex, where N denotes the number of vertices in TQ(n). Moreover, all independent spanning trees rooted at an arbitrary vertex constructed by our construction method are isomorphic and the height of each tree is n + 1 for any integer n >= 2. (C) 2011 Elsevier Inc. All rights reserved.