The average connectivity of a digraph☆

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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 29 and at most 12.

MSC

05C40
05C20
05C05
68R10

Keywords

Average connectivity
Oriented graphs
Oriented trees
Tournaments

Cited by (0)

☆

The authors wish to thank the referees for their helpful comments.

1

Research supported in part by the South African National Research Foundation and the University of Natal.

2

Research supported by an NSERC Canada Grant.

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