On the parity of the Wiener index

Stephan Wagner; Hua Wang

doi:10.1016/j.ejc.2008.06.004

On the parity of the Wiener index

Stephan Wagner, Hua Wang

Mathematical Sciences

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	996-1004
Number of pages	9
Journal	European Journal of Combinatorics
Volume	30
Issue number	4
DOIs	https://doi.org/10.1016/j.ejc.2008.06.004
State	Published - May 2009

Scopus Subject Areas

Discrete Mathematics and Combinatorics

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10.1016/j.ejc.2008.06.004

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AB - 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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M3 - Article

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JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

IS - 4

ER -

On the parity of the Wiener index

Abstract

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