Circuit-switched routings for automorphisms of a hypercube

We consider, for d>1, a directed d-dimensional hypercube, Q_d=(V,E), where V is a set of 2^d nodes, each denoted by a distinct binary string of length , and E is the set of edges (x,y), such that x,yεV differ in exactly one position of their bit strings. Given a permutation of the vertices of Q_d, which describes a source-destination mapping, we study the existence of a set of paths from each source to each destination such that no edge of Q_d is assigned to more than one path. For a multiprocessor connected in such a manner, such a set of paths could be used for circuit switching of messages between source destination processors (nodes). We show that for any automorphism of Q_d there is such a set of paths