R. Merris, An edge version of the matrix-tree theorem and the Wiener index, Linear & Multilinear Algebra 25 (1989), 291-296. Math Reviews 91g: 05096. Research supported by ONR contract 85K0335.

It follows from the main result of this article that the chemical Wiener index (see, e.g., [D. H. Rouvray, Predicting chemistry from topology, Scientific American 255 (Sept. 1986), 40-47]) of a tree on n vertices is n times the sum of the reciprocals of its positive Laplacian eigenvalues. If G is a tree, the smallest positive Laplacian eigenvalue, a(G), is called the "algebraic connectivity". Because W'(G) = n/a(G) is the dominant term in the aforementioned sum, the author speculated that W'(G) might be a useful chemical index. (This speculation was nicely reinforced in [D. J. Klein, Graph geometry, graph metrics, and Wiener, MATCH 35 (1997), 7-27].) Among the publications referencing this article are

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