Super-Arc-Connected and Super-Connected Total Digraphs

Abstract

Let \(D\) be a strongly connected digraph with order at least two. Let \(T(D)\) denote the total digraph of \(D\), and let \(\kappa(D)\) and \(\lambda(D)\) denote the connectivity and arc-connectivity of \(D\), respectively. In this paper, we study super-arc-connected and super-connected total digraphs. The following results are obtained:

1. \(T(D)\) is super-arc-connected if and only if \(D \ncong \overrightarrow{K_2}\).
2. If \(\kappa(D) + \lambda(D) > \delta(D) + 1\), then \(T(D)\) is super-connected.