The Hosoya Index, Lucas Numbers, and QSPR

The 2-methyl alkanes, the cyclic alkanes, and the 1-methyl bicyclo[X.1.0] alkanes are shown to possess identical values for the Hosoya index. For these specific molecular graphs, this topological index generates the integer sequence known as Lucas numbers. The implication of these results for quantitative structure-property relationship development is illustrated using normal boiling point data.