On The Super-Restricted Arc-Connectivity Of S-Geodetic Digraphs

For a strongly connected digraph D the restricted arc-connectivity lambda'(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 every digraph on at least 4 vertices and of minimum degree at least 2 is lambda' -connected and lambda'(D) <=xi'(D), where xi'(D) is the minimum arc-degree of D. Also in this paper we introduce the concept of super- lambda' digraphs and provide a sufficient condition for an s -geodetic digraph to be super- lambda'. Further, we show that the h -iterated line digraph Lh(D) of an s -geodetic digraph is super- lambda' for a particular h. (c) 2012 Wiley Periodicals, Inc. NETWORKS, 2013