Generalized spectral moments of the iterated line graphs sequence. A novel approach to QSPR studies

The spectral moments of the iterated line graph sequence (ILGS) are defined and expressed in terms of structural fragments of the molecular graphs, i.e., embedding frequencies. Several mathematical expressions to find some embedding frequencies of trees are given in terms of the spectral moments of the ILGS. This iterative method was permitted to obtain 12 embedding frequencies of alkanes with up to nine carbon atoms. These embedding frequencies and the spectral moments of the ILGS are used to describe seven important physicochemical properties of alkanes. It was proven that the spectral moments of the ILGS produce high quality QSPR models. This approach showed significant improvements in the statistical parameters of the regressions in comparison to the models obtained with the embedding frequencies. Most of the regression models obtained with the spectral moments of the ILGS can be considered as the best QSPR models reported up to now to describe these physicochemical properties of alkanes.