Super-connected and super-arc-connected Cartesian product of digraphs

We study the super-connected, hyper-connected and super-arc-connected Cartesian product of digraphs. The following two main results will be obtained:(i)If δ+(Di)=δ−(Di)=δ(Di)=κ(Di) for i=1,2, then D1×D2 is super-κ if and only if ,(ii)If δ+(Di)=δ−(Di)=δ(Di)=λ(Di) for i=1,2, then D1×D2 is super-λ if and only if , where λ(D)=δ(D)=1, denotes the complete digraph of order n and n⩾2.