On the Parity of the Wiener Index of Trees

Document Type

Article

Publication Date

5-2009

Publication Title

European Journal of Combinatorics

DOI

10.1016/j.ejc.2008.06.004

ISSN

0195-6698

Abstract

It is a known fact that the Wiener index (i.e. the sum of all distances between pairs of vertices in a graph) of a tree with an odd number of vertices is always even. In this paper, we consider the distribution of the Wiener index and the related tree parameter “internal path length” modulo 2 by means of a generating functions approach as well as by constructing bijections for plane trees.

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