IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

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 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 nonleaf vertices. The Wiener index conjecture for trees then follows from this and the computational results in [8] and [5].

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