Directed Tree Connectivity of Symmetric Digraphs and Complete Bipartite Digraphs

Abstract

Sun and Yeo introduced the concept of directed tree connectivity, including the generalized [Formula: see text]-vertex-strong connectivity, [Formula: see text] and generalized [Formula: see text]-arc-strong connectivity, [Formula: see text] [Formula: see text], which could be seen as a generalization of classical connectivity of digraphs and a natural extension of the well-established undirected tree connectivity. In this paper, we study the directed tree connectivity of symmetric digraphs and complete bipartite digraphs. We give lower bounds for the two parameters [Formula: see text] and [Formula: see text] on symmetric digraphs. We also determine the precise values of [Formula: see text] for every [Formula: see text] and [Formula: see text] for [Formula: see text], where [Formula: see text] is a complete bipartite digraph of order [Formula: see text].