Restricted arc-connectivity of generalized p-cycles

Abstract For 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 D 1 such that D − V ( D 1 ) contains an arc. In this paper we prove that a generalized p -cycle is λ ′ -optimal if diam ( D ) ≤ 2 l + 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 ) ≤ 2 l + 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 .