The Partial Line Digraph Technique in the Design of Large Interconnection Networks

The following problem arises in the design of some interconnection networks for distributed systems. Namely, to construct digraphs with given maximum out-degree, reduced diameter, easy routing, good connectivity, and good expand-ability. To this end, a new method based on the concept of partial line digraph is presented. This proposal, which turns out to be a generalization of the so-called line digraph technique, allows us to obtain digraphs that satisfy all the above-mentioned requirements. In particular it is shown that the partial line di-graphs of Kautz digraphs solve the (d. digraph problem-i.e. to minimize the diameter D in a digraph of maximum out-degree d and number of vertices S-for any in the range