On the super-restricted arc-connectivity of s -geodetic digraphs

Authors:
Camino Balbuena;Pedro García-Vázquez;Adriana Hansberg;Luis Pedro Montejano
Affiliations:
Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya, E08034-Barcelona, Spain;Departamento de Matemática Aplicada I, Universidad de Sevilla, E41012-Sevilla, Spain;Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya, E08034-Barcelona, Spain;Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya, E08034-Barcelona, Spain
Venue:
Networks
Year:
2013

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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 © 2013 Wiley Periodicals, Inc.