Broadcasting on faulty hypercubes

In this paper we propose a method for constructing the maximum number of edge-disjoint spanning trees (in the directed sense) on a hypercube with arbitrary one faulty node. Each spanning tree is of optimal height. By taking the common neighbor of the roots of these edge-disjoint spanning trees as the new root and reversing the direction of the directed link from each root to the new root, a spanning graph, consisting of n-1 edge-disjoint spanning trees of optimal height is formed. Broadcasting based on the spanning graph has an optimal bandwidth utilization and an optimal latency.