An Algorithm to Find Optimal Independent Spanning Trees on Twisted-Cubes

Abstract

Multiple independent spanning trees have applications to fault tolerance and data broadcasting in distributed networks. There is a conjecture on independent spanning trees: any n-connected graph has n independent spanning trees rooted at an arbitrary vertex. The conjecture has been confirmed only for n-connected graphs with n=4, and it is still open for arbitrary n-connected graphs when n ≥ 5. In this paper, we provide a construction algorithm to find n independent spanning trees for the n-dimensional twisted-cube TN <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> , where N denotes the number of vertices in TN <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> . And for n ≥ 3, the height of each independent spanning tree on TN <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> is n+1.