Article
All but 49 Numbers are Wiener Indices of Trees
Acta Applied Mathematica
(2006)
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>108 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].
Keywords
- Wiener indices,
- Trees
Disciplines
Publication Date
May, 2006
DOI
10.1007/s10440-006-9037-2
Citation Information
Hua Wang and Guang Yu. "All but 49 Numbers are Wiener Indices of Trees" Acta Applied Mathematica Vol. 92 Iss. 1 (2006) p. 15 - 20 ISSN: 1572-9036 Available at: http://works.bepress.com/hua_wang/141/