The average connectivity of a digraph

  • Authors:

  • Michael A. Henning;Ortrud R. Oellermann

  • Affiliations:

  • School of Mathematics, Statistics, & Information Technology, University of Natal, Private Bag X01, Pietermaritzburg 3209, South Africa;Department of Mathematics and Statistics, The University of Winnipeg, 515 Portage Avenue, Winnipeg, MB R3B 2E9, Canada

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2004

  • Optimal orientation on-line

    SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science

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Abstract

In this paper we consider the concept of the average connectivity of a digraph D defined to be the average, over all ordered pairs (u,v) of vertices of D, of the maximum number of internally disjoint directed u-v paths. We determine sharp bounds on the average connectivity of orientations of graphs in terms of the number of vertices and edges and for tournaments and orientations of trees in terms of their orders. An efficient procedure for finding the maximum average connectivity among all orientations of a tree is described and it is shown that this maximum is always greater than 2/9 and at most ½.