Abstract
A novel index based on the hyper-Wiener index, named Lu, was proposed. The relative bond length between two adjacent vertices in a molecular graph was taken into account in the definition of the Lu index. The usefulness of the new index in QSPR study was verified by its correlation with a number of organic compounds including aliphatic aldehydes and ketones. For each of the physical properties (the normal boiling points, molar refractions and gas heat capacities at 25°C), high quality QSPR models were obtained. The final models were validated to be statistically reliable using the leave-one-out cross validation and/or an external test set. The correlation coefficients (> 0.99) of all constructed models indicate the necessity of such an index, and show the potential of the Lu index for QSAR/QSPR studies.
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