Abstract

A connected digraph is said to be superconnected if it is maximally connected and every minimum disconnecting set F consists of the vertices adjacent to or from a given vertex not belonging to F. Let δ be the minimum degree of the digraph and π be a positive integer such that πδ/2 when δ7, or π(δ-2)/2 for δ5. We prove that G is maximally connected or has a good superconnectivity if the diameter D2ℓ^π-2 and ℓ⁰2, where ℓ^π is a generalization of the semigirth ℓ⁰ introduced by Fàbrega and Fiol (J. Graph Theory 13(6) (1989) 657). We also show that G is maximally connected if π(δ-1)/2 and 3δ6. In the edge case, it is enough that D2ℓ^π-1. Finally, the obtained results are applied to the iterated line digraphs.

Keywords: Connectivity; Superconnectivity; Cutset; Digraph; Line digraph; Semigirth

MSC: 05C40; 05C20

Article Outline

1. Introduction

2. Moving away from a subset of vertices

3. Diameter constraints

References

Research supported by the Ministry of Science and Technology, Spain, the European Regional Development Fund (ERDF) under projects TIC-2000-1017 and TIC-2001-2171.