Line digraph iterations and the (d,k) problem for directed graphs

Authors:
M. A. Fiol;I. Alegre;J. L.A. Yebra
Affiliations:
-;-;-
Venue:
ISCA '83 Proceedings of the 10th annual international symposium on Computer architecture
Year:
1983

Citing 1
Cited 5

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Graph Theory with Applications to Engineering and Computer Science (Prentice Hall Series in Automatic Computation)

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European Journal of Combinatorics

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Abstract

We consider in this paper the (d,k) problem for directed graphs: to maximize the number of vertices in a digraph of degree d and diameter k. For any values of d and k, we construct a graph with a number of vertices larger than (d 2−1)/d2 times the (non-attainable) Moore bound. In particular, this solves the (d,k) digraph problem for k&equil;2. We also show that these graphs can be obtained as line digraph iterations and that this technique provides us with a simple local routing algorithm for the corresponding networks.