## All but 49 numbers are Wiener indices of trees

**A 2005 Preprint by
H. Wang and
G. Yu
**

- 2005:01
The Wiener index is one of the main descriptors that correlate a chemical compoundâ€™s molecular graph with experimentally gathered data regarding the compoundâ€™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 nonleaf vertices. The Wiener index conjecture for trees then follows from this and the computational results in [8] and [5].