1985/12/01 by E. Rodney Canfield, Robert W. Robinson, Dennis H. Rouvray · 60 citations
Mathematics · Computer Science · Chemistry · #Graph theory and applications #Computational Drug Discovery Methods #Synthesis and Properties of Aromatic Compounds #Wiener index #Branching (polymer chemistry) #Combinatorics #Mathematics #Tree (set theory) #Recursion (computer science) #Weighting #Graph #Discrete mathematics #Chemistry #Physics #Algorithm
paper · doi:10.1002/jcc.540060613
published in Journal of Computational Chemistry 6(6), 598-609 (Wiley)
openalex publication_date 1985/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21
Abstract The many applications of the distance matrix, D(G), and the Wiener branching index, W(G), in chemistry are briefly outlined. W(G) is defined as one half the sum of all the entries in D(G). A recursion formula is developed enabling W(G) to be evaluated for any molecule whose graph G exists in the form of a tree. This formula, which represents the first general recursion formula for trees of any kind, is valid irrespective of the valence of the vertices of G or of the degree of branching in G. Several closed expressions giving W(G) for special classes of tree molecules are derived from the general formula. One illustrative worked example is also presented. Finally, it is shown how the presence of an arbitrary number of heteroatoms in tree‐like molecules can readily be accommodated within our general formula by appropriately weighting the vertices and edges of G.