Minimal strong digraphs

TL;DR

This paper introduces a method for constructing minimal strong digraphs through expansion, characterizes their properties, and provides algorithms for generating and classifying these digraphs and their spectral classes.

Contribution

It presents a new expansion-based framework for sequentially constructing minimal strong digraphs and characterizes their properties and classifications.

Findings

Every minimal strong digraph can be obtained by expansion from a smaller one.

Sequential procedures for constructing minimal strong digraphs are provided.

Algorithms for computing unlabeled minimal strong digraphs and their isospectral classes are described.

Abstract

We introduce adequate concepts of expansion of a digraph to obtain a sequential construction of minimal strong digraphs. We characterize the class of minimal strong digraphs whose expansion preserves the property of minimality. We prove that every minimal strong digraph of order $n\geq 2$ 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.