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Determination of the Wiener molecular branching index for the general tree
Author(s) -
Canfield E. R.,
Robinson R. W.,
Rouvray D. H.
Publication year - 1985
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540060613
Subject(s) - wiener index , branching (polymer chemistry) , combinatorics , mathematics , tree (set theory) , recursion (computer science) , weighting , graph , discrete mathematics , chemistry , physics , algorithm , organic chemistry , acoustics
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.