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doi:10.1016/0012-365X(93)90545-5 
Copyright © 1993 Published by Elsevier Science B.V. All rights reserved.
Symmetric routings of the hypercube*1
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Received 7 December 1991.
Abstract
In this paper we prove that, for any n and k such that (k−1)Ckn is even, there exists a set of shortest paths between all the pairs of vertices at distance k of an n-cube such that each vertex is on the same number of paths. We conjecture that there also exists such a set of paths where each edge is on the same number of paths, and we prove it for k odd or k=2 or 4. If (k−1)Ckn is odd, we prove that the numbers of paths going through all vertices (edges) differ of at most by one (two). We then give the same kind of results for paths between all pairs of vertices.
Article Outline
*1 This work was done with the support of the French GRECO-PRC C3.
Correspondence to: Domique Sotteau, LRI Bat 490, Universite Paris-Sud, 91405 Orsay Cedex, France.
