Acta Applicandae Mathematica

, Volume 92, Issue 1, pp 15–20

All but 49 Numbers are Wiener Indices of Trees


DOI: 10.1007/s10440-006-9037-2

Cite this article as:
Wang, H. & Yu, G. Acta Appl Math (2006) 92: 15. doi:10.1007/s10440-006-9037-2


The Wiener index is one of the main descriptors that correlate a chemical compound’s molecular graph with experimentally gathered data regarding the compound’s characteristics. A long standing conjecture on the Wiener index ([4, 5]) states that for any positive integer \(n\) (except numbers from a given 49 element set), one can find a tree with Wiener index \(n\). In this paper, we prove that every integer \(n>10^8\) is the Wiener index of some short caterpillar tree with at most six non-leaf vertices. The Wiener index conjecture for trees then follows from this and the computational results in [8] and [5].

Mathematics Subject Classification (2000)


Key words

trees Wiener index molecular graph 

Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA
  2. 2.Department of MathematicsUniversity of South CarolinaColumbiaUSA

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