On large vertex-symmetric digraphs

Abstract

There is special interest in the design of large vertex-symmetric graphs and digraphs as models of interconnection networks for implementing parallelism. In these systems, a large number of nodes are connected with relatively few links and short paths between the nodes, and each node may execute the same communication software without modifications. In this paper, a method for obtaining new general families of large vertex-symmetric digraphs is put forward. To be more precise, from a k -reachable vertex-symmetric digraph and another ( k + 1 ) -reachable digraph related to the previous one, and using a new special composition of digraphs, new families of vertex-symmetric digraphs with small diameter are presented. With these families we obtain new vertex-symmetric digraphs that improve various values of the table of the largest known vertex-symmetric ( Δ , D ) -digraphs. The paper also contains the ( Δ , D ) -table for vertex-symmetric digraphs, for Δ ≤ 13 and D ≤ 12 .