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All but 49 Numbers are Wiener Indices of Trees

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Abstract

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].

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Article 26 June 2018

Tomislav Došlić, Ivica Martinjak, … Ivana Zubac

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Authors and Affiliations

  1. Department of Mathematics, University of Florida, Gainesville, FL, 32611, USA

    Hua Wang

  2. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    Guang Yu

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  1. Hua Wang
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  2. Guang Yu
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Correspondence to Hua Wang.

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This research was supported in part by the NSF contracts Nr. 0072187 and 0302307.

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Wang, H., Yu, G. All but 49 Numbers are Wiener Indices of Trees. Acta Appl Math 92, 15–20 (2006). https://doi.org/10.1007/s10440-006-9037-2

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  • DOI: https://doi.org/10.1007/s10440-006-9037-2

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