Vertex-symmetric Digraphs with Small Diameter

There is increasing interest in the design of dense vertex-symmetric graphs and digraphs as models of interconnection networks for implementing parallelism. In these systems many nodes are connected with relatively few links and short paths between them and each node may execute, without modifications, the same communication software. In this paper we give new families of dense vertex-symmetric (A, D) digraphs, that is large digraphs with a given maximum out-degree A and diameter at most D. The digraphs are derived from a certain family of digraphs on alphabets, proposed by Faber and Moore (1988), with new construction techniques that generalize previous results from Conway and Guy (1982). With these families we have made important updates in the table of largest known vertex-symmetric (A, D) digraphs.