Line digraph iterations and the (d,k) digraph problem
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This paper studies the behavior of the diameter and the average distance between vertices of the line digraph of a given digraph. The results obtained are then applied to the so-called (d, k) digraph problem, that is, to maximize the number of vertices in a digraph of maximum out-degree d and diameter k. By line digraph iterations it is possible to construct digraphs with a number of vertices larger than (d2 - l)/d2 times the (nonattainable) Moore bound. In particular, this solves the (d, k) digraph problem for k = 2. Also, the line digraph technique provides us with a simple local routing algorithm for the corresponding networks.
CitationFiol, M. A.; Andrés, J.; Alegre, I. Line digraph iterations and the (d,k) digraph problem. "IEEE transactions on computers", Maig 1984, vol. C-33, núm. 5, p. 400-403.
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