λ′-optimal digraphs

Restricted arc-connectivity is a more refined network reliability index than arc-connectivity. In this paper, we first introduce the concept of minimum arc-degree and show for many digraphs, the minimum arc-degree is an upper bound on the restricted arc-connectivity. Next we call a strongly connected digraph a λ′-optimal digraph if its restricted arc-connectivity is equal to its minimum arc-degree. Finally, we give some sufficient conditions for a digraph to be λ′-optimal.