On the parity of the Wiener index

Stephan Wagner, Hua Wang

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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.

Original languageEnglish
Pages (from-to)996-1004
Number of pages9
JournalEuropean Journal of Combinatorics
Volume30
Issue number4
DOIs
StatePublished - May 2009

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