Minimal strong digraphs

We introduce adequate concepts of expansion of a digraph to obtain a sequential construction of minimal strong digraphs. We characterize the necessary and sufficient condition for an external expansion of a minimal strong digraph to be a minimal strong digraph. We prove that every minimal strong digraph of order n >= 2 is the expansion of a minimal strong digraph of order n - 1 and we give sequentially generative procedures for the constructive characterization of the classes of minimal strong digraphs. Finally we describe algorithms to compute unlabeled minimal strong digraphs and their isospectral classes. (C) 2011 Elsevier B.V. All rights reserved.