Distances in random trees

Abstract: The Wiener index of a graph G is defined as the sum of the distances between all pairs of vertices in G. In this master thesis we introduce recursive trees, plane oriented recursive trees (PORTs) and simply generated trees. We then present results by Neininger, Janson, and Munsonius and Rüschendorf for the expectation and limiting distribution of the Wiener index of these families. For recursive trees and PORTs the results follow from analysing the recursive structure of the trees and the contraction method, while the results for simply generated trees is based on a limiting object, the continuum random tree.