Maximally connected digraphs

Abstract

This paper introduces a new parameter I = I(G) for a loopless digraph G, which can be thought of as a generalization of the girth of a graph. Let k, λ, δ, and D denote respectively the connectivity, arc‐connectivity, minimum degree, and diameter of G. Then it is proved that λ = δ if D ⩽ 2I and κ k = δ if D ⩽ 2I ‐ 1. Analogous results involving upper bounds for k and λ are given for the more general class of digraphs with loops. Sufficient conditions for a digraph to be super‐λ and super‐k are also given. As a corollary, maximally connected and superconnected iterated line digraphs and (undirected) graphs are characterized. Copyright © 1989 Wiley Periodicals, Inc., A Wiley Company