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Determination of the Wiener molecular branching index for the general tree

✍ Scribed by E. R. Canfield; R. W. Robinson; D. H. Rouvray

Publisher
John Wiley and Sons
Year
1985
Tongue
English
Weight
928 KB
Volume
6
Category
Article
ISSN
0192-8651

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✦ Synopsis

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.

πŸ“œ SIMILAR VOLUMES

The generalized Randić index of trees
The generalized Randić index of trees
✍ Paul Balister; BΓ©la BollobΓ‘s; Stefanie Gerke πŸ“‚ Article πŸ“… 2007 πŸ› John Wiley and Sons 🌐 English βš– 241 KB

## Abstract The generalized Randić; index ${R}\_{-\alpha}(T)$ of a tree __T__ is the sum over the edges ${u}{v}$ of __T__ of $(d(u)d(v))^{-\alpha}$ where ${d}(x)$ is the degree of the vertex __x__ in __T__. For all $\alpha > 0$, we find the minimal constant $\beta\_{0}=\beta\_{0}(\alpha)$ such that