Characterization of Minimum Restricted Arc-Cuts of Unidirectional Star Graphs

For a strongly connected digraph [Formula: see text], the restricted arc-connectivity [Formula: see text] is the minimum cardinality of all restricted arc-cuts [Formula: see text] where [Formula: see text] has a non-trivial strong component [Formula: see text] and [Formula: see text] contains an arc. A restricted arc-cut [Formula: see text] of [Formula: see text] is called a minimum restricted arc-cut if [Formula: see text]. A strongly connected digraph [Formula: see text] is hyper-[Formula: see text] if the removal of any minimum restricted arc-cut [Formula: see text] of [Formula: see text] such that [Formula: see text] has exactly one non-trivial strong component [Formula: see text], and [Formula: see text] only contains an arc. In this paper, we prove that unidirectional star graph [Formula: see text] is hyper-[Formula: see text] for [Formula: see text].