Graphs & digraphs (2nd ed.)
Strategies for interconnection networks: some methods from graph theory
Journal of Parallel and Distributed Computing
Line digraph iterations and the (d,k) problem for directed graphs
ISCA '83 Proceedings of the 10th annual international symposium on Computer architecture
Superfluous edges and exponential expansions of De Bruijn and Kautz graphs
Discrete Applied Mathematics
Low Diameter Interconnections for Routing in High-Performance Parallel Systems
IEEE Transactions on Computers
Theory and network applications of balanced kautz tree structures
ACM Transactions on Internet Technology (TOIT)
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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 expandability. To this end, a 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 digraphs that satisfy all the above-mentioned requirements to be obtained. In particular, it is shown that the partial line digraphs of Kautz digraphs solve the (d, N) digraph problem, i.e. to minimize the diameter D in a digraph of maximum out-degree d and number of vertices N, for any N in the range d/sup D-1/+d/sup D-2/+. . .+1or=Nor=d/sup D/+d/sup D-1/.