Restricted connectivity of total digraph

For a strongly connected digraph D = (V (D),A(D)), an arc-cut S ⊆ A(D) is a k-restricted arc-cut of D if D − S has at least two strong components of order at least k. The k-restricted arc-connectivity λk(D) is the minimum cardinality of all k-restricted arc-cuts. The k-restricted vertex-connectivity κk(D) can be defined similarly. In this paper, we provide upper and lower bounds for λ2 and κ2 for the total digraph T(D) of D.