Drugs and other chemical compounds are often modeled as polygonal shapes called the molecular graph, which can be a path, a tree, or in general any graph. An indicator defined over this molecular graph, the Wiener index, has been shown to be strongly correlated to various chemical properties of the compound. The Wiener index conjecture for trees states that for any integer n (except for a finite set), one can find a tree with Wiener index n. In this paper, we present progress towards proving this conjecture by presenting a 4-parameter family of trees that we show experimentally to affirm the Wiener index conjecture for very large values of n. Given an integer n, we also present efficient algorithms for finding the tree whose Wiener index is n.
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