All but 49 numbers are Wiener indices of trees
by
Hua Wang
Department of Mathematics, University of South Carolina, Columbia, SC, 29208
Coauthors: Gang Yu, Department of Mathematics, University of South Carolin, Columbia, SC, 29208

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 states that for any positive integer n (except numbers from a given 49 element set), one can find a tree with Wiener index n. 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 some computational results.

Date received: March 14, 2005