The Wiener Index of Random Trees

Wiener index of random trees

The Wiener Index of Random Digital Trees

The Wiener index has been studied for simply generated random trees, non-plane unlabeled random trees and a huge subclass of random grid trees containing random binary search trees, random medianof-(2k+ 1) search trees, random m-ary search trees, random quadtrees, random simplex trees, etc. An important class of random grid trees for which the Wiener index was not studied so far are random digi...

The Wiener Index Of Random Trees

The Wiener index is analyzed for random recursive trees and random binary search trees in the uniform probabilistic models. We obtain the expectations, asymptotics for the variances, and limit laws for this parameter. The limit distributions are characterized as the projections of bivariate measures that satisfy certain fixed-point equations. Covariances, asymptotic correlations, and bivariate ...

On the Wiener index of random trees

By a theorem of Janson, the Wiener index of a random tree from a simply generated family of trees converges in distribution to a limit law that can be described in terms of the Brownian excursion. The family of unlabelled trees (rooted or unrooted), which is perhaps the most natural one from a graph-theoretical point of view, since isomorphisms are taken into account, is not covered directly by...

The Wiener Index of simply generated random trees

Asymptotics are obtained for the mean, variance and higher moments as well as for the distribution of the Wiener index of a random tree from a simply generated family (or, equivalently, a critical Galton– Watson tree). We also establish a joint asymptotic distribution of the Wiener index and the internal path length, as well as asymptotics for the covariance and other mixed moments. The limit l...