Minimum k-geodetically connected digraphs

  • Authors:

  • Ján Plesník

  • Affiliations:

  • Department of Numerical and Optimization Methods, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynska dolina, 84248 Bratislava, Slovakia

  • Venue:
  • Networks
  • Year:
  • 2004

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Abstract

A strong digraph is k-geodetically connected (k-GC) if the removal of at least k vertices is required to increase the distance between at least one pair of vertices or reduce it to a single vertex. Such digraphs can serve as models of distance invulnerable networks (immune to k – 1 or fewer vertex failures) for a system with one-way communications. For every integer n, we determine the minimum size 2-GC digraphs of order n. Further, we find the minimum size of a k-GC digraph of order n if n ≡ 0 (mod k) and give good bounds for all n. Also, several operations on and constructions of k-GC digraphs are presented. We show that the problem of finding a minimum size k-GC spanning subdigraph of a given digraph is NP-hard. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(4), 243–253 2004