Variation of Adriatic and Wiener indices for different cycle lengths and paths

The outcome of a transformation of chemical structure into mathematical model results in numerical descriptor. The chemical compound of a molecule is encoded into a useful number called molecular descriptor. These numerical descriptors have significant importance in the applications of physico-chemical properties of QSAR/QSPR/QSTR studies. Motivated by the work of Vukicevic, Wiener index and Adriatic index are determined for a path attached to cycles of length >= 3. The attached cycle is gradually moved through the set of vertices of the path to study the variation of the Wiener index. It is found that the Adriatic index is equal for all such graphs but the Wiener index, however, appears to be different in every case and lengths.