Topological index and thermodynamic properties. 5. How can we explain the topological dependency of thermodynamic properties of alkanes with the topology of graphs?

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.