On the super‐restricted arc‐connectivity of s ‐geodetic digraphs
Camino Balbuena, P. García‐Vázquez, Adriana Hansberg, Luis Pedro Montejano · Networks · 2012
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 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 λ′ ‐connected and λ′(D) ≤ξ′(D), where ξ′(D) is the minimum arc‐degree of D. Also in this paper we introduce the concept of super‐ λ′ digraphs and provide a sufficient condition for an s ‐geodetic digraph to be super‐ λ′. Further, we show that the h ‐iterated line digraph Lh(D) of an s ‐geodetic digraph is super‐ λ′ for a particular h. © 2012 Wiley Periodicals, Inc. NETWORKS, 2013