The Wiener Index of Random Digital Trees

Project: Probabilistic Analysis of Random Digital Trees

This is the final report on the National Science Council project “Probabilistic Analysis of Random Digital Trees” with grant number NSC-99-2115-M-009-007-MY2. We first summarize the main achievements of the project. • We applied our approach from the project proposal to various cost measures in random symmetric digital search trees (see [7]). • We applied our approach to partial match retrieval...

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 ...

Wiener index of random trees

Peripheral Wiener Index of a Graph

The eccentricity of a vertex $v$ is the maximum distance between $v$ and anyother vertex. A vertex with maximum eccentricity is called a peripheral vertex.The peripheral Wiener index $ PW(G)$ of a graph $G$ is defined as the sum ofthe distances between all pairs of peripheral vertices of $G.$ In this paper, weinitiate the study of the peripheral Wiener index and we investigate its basicproperti...

Limit theorems for depths and distances in weighted random b-ary recursive trees

Limit theorems are established for some functionals of the distances between two nodes in weighted random b-ary recursive trees. We consider the depth of the nth node and of a random node, the distance between two random nodes, the internal path length and the Wiener index. As application these limit results imply by an imbedding argument corresponding limit theorems for further classes of rand...