Edge-independent spanning trees in augmented cubes

Edge-independent spanning trees (EISTs) have important applications in networks such as reliable communication protocols, one-to-all broadcasting, and secure message distribution, thus their designs in several classes of networks have been widely investigated. The n-dimensional augmented cube (AQn) is an important variant of the n-dimensional hypercube. It is (2n1)-regular, (2n1)-connected (n3), vertex-symmetric and has diameter of n/2. In this paper, by proposing an O(NlogN) algorithm that constructs 2n1 EISTs in AQn, where N is the number of nodes in AQn, we solve the EISTs problem for this class of graphs. Since AQn is (2n1)-regular, the result is optimal with respect to the number of EISTs constructed.

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