Precise Values for the Strong Subgraph 3-Arc-Connectivity of Cartesian Products of Some Digraph Classes

Abstract

Let [Formula: see text] be a digraph of order [Formula: see text], [Formula: see text] a subset of [Formula: see text] of size [Formula: see text] and [Formula: see text]. A strong subgraph [Formula: see text] of [Formula: see text] is called an [Formula: see text]-strong subgraph if [Formula: see text]. A pair of [Formula: see text]-strong subgraphs [Formula: see text] and [Formula: see text] is said to be arc-disjoint if [Formula: see text]. Let [Formula: see text] be the maximum number of arc-disjoint [Formula: see text]-strong subgraphs in [Formula: see text]. Sun and Gutin defined the strong subgraph [Formula: see text]-arc-connectivity as [Formula: see text] The new parameter [Formula: see text] could be seen as a generalization of classical edge-connectivity of undirected graphs. In this paper, we get precise values for the strong subgraph 3-arc-connectivity of Cartesian products of some digraph classes. Also, we prove that there is no upper bound on [Formula: see text] depending on [Formula: see text] and [Formula: see text].