The restricted arc connectivity of Cartesian product digraphs

For a strongly connected digraph D=(V(D),A(D)), an arc set S⊆A(D) is a k-restricted arc cut if D−S has a non-trivial strongly connected component D1 such that D−V(D1) contains an arc. The restricted arc connectivity λ′(D) is the minimum cardinality of all restricted arc-cuts. In this paper we prove that Cartesian product digraph D=D1×D2 of two strongly connected digraphs D1 and D2 is λ′-connected. We also give an upper and lower bound for λ′(D), respectively. Furthermore, we obtain that and .