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A class of graph invariants known today as topological indices are being increasingly realized by chemists and others to be powerful tools in the description of chemical phenomena. Topological indices generally characterize both the size and shape of chemical species; in recent years a number of such indices have been put forward that sensitively reflect the amount of branching present in molecules. Chemists are thus able to model accurately the chemical behavior of an extensive range of chemical substances in all three thermodynamic states. In discussing the manifold applications of topological indices to the description of physicochemical properties, we present a survey of the progress to date in this area and point out some of the advantages and drawbacks of using topological indices.

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