Restricted arc-connectivity of generalized p-cycles

AbstractFor a strongly connected digraph D the restricted arc-connectivity λ′(D) is defined as the minimum cardinality of an arc-cut over all arc-cuts S satisfying that D−S has a non-trivial strong component D1 such that D−V(D1) contains an arc. In this paper we prove that a generalized p-cycle is λ′-optimal if diam(D)≤2ℓ+p−2, where ℓ is the semigirth of D and p≥3. Further we show that the k-iterated line digraph is λ′-optimal if diam(D)≤2ℓ+p−2+k for p≥3. We improve these results for p large enough and we also improve known results on super-λ for p-cycles with p≥3