Correlations between the thermodynamic properties of alkanes and topological indices of integer values (ITI) for the corresponding graphs are studied. A set of higher order Z-indices, Z n , for n-step graphs, G n , are newly defined. Fairly good correlation with the density of liquid was obtained for a single index Z 3, representing the static topology of alkane molecules. For the boiling point, which is determined by the dynamical motion of molecules, the quantity, 4Z 1 + Z 3, was shown to have remarkably good correlation among other combinations of ITI's. Physicochemical interpretations of these correlation problems are given.

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