PC Seminar: The Terminal Wiener index of random recursive trees

Abstract: The Terminal Wiener index of a rooted tree is defined as the sum of all pair- wise distances between leaves in the tree. It was introduced in 2009 by Gutman, Furtula and Petrović, motivated by potential applications in chemistry. For the regular Wiener index, in which the sum is taken over all pairs of vertices instead of pairs of leaves, various results regarding its behaviour in different types of trees have been shown by, among others, Janson, Wagner and Neininger. In contrast to this, very few results exist regarding the Terminal Wiener index. In this talk, we show that for random recursive trees the average distance between leaves and the average distance between vertices is small, which corresponds to the behaviour of the Terminal- and regular Wiener indices. Additionally, we also present similar results for conditioned Galton-Watson trees.

Participte on site or via Zoom link (meeting ID 65089679653).

This is a seminar in our seminar series on Probability and Combinatorics (PC).