Average distance in k-connected tournaments

The average distance μ(D) of a strong digraph D is the average of the distances between all ordered pairs of distinct vertices of D. Plesníc [6] proved that if D is a strong tournament of order n, then μ(D) ≤ n+4/6 + 1/n. In this paper, we show that if D is a k-connected tournament of order n, then μ(D) < n/6k + 19/6 + k/n. We demonstrate that, apart from an additive constant, this bound is best possible.