Restricted arc-connectivity of digraphs

  • Authors:

  • Lutz Volkmann

  • Affiliations:

  • Lehrstuhl II für Mathematik, RWTH Aachen University, 52056 Aachen, Germany

  • Venue:
  • Information Processing Letters
  • Year:
  • 2007

Quantified Score

Hi-index 0.90

Visualization

Abstract

Since interconnection networks are often modeled by graphs or digraphs, the edge-connectivity of a graph or arc-connectivity of a digraph are important measurements for fault tolerance of networks. The restricted edge-connectivity @l^'(G) of a graph G is the minimum cardinality over all edge-cuts S in a graph G such that there are no isolated vertices in G-S. A connected graph G is called @l^'-connected, if @l^'(G) exists. In 1988, Esfahanian and Hakimi [A.H. Esfahanian, S.L. Hakimi, On computing a conditional edge-connectivity of a graph, Inform. Process. Lett. 27 (1988), 195-199] have shown that each connected graph G of order n=4, except a star, is @l^'-connected and satisfies @l^'(G)=