Chemical significance and degeneracy of weighted degree-based topological descriptor second Davan index for octane isomers and computation of certain nanostructures

This study introduces a novel topological descriptor, the second Davan index (SDI) based on weighted degree of molecular graphs. Its chemical significance is validated through QSPR modelling of octane isomers, where it exhibits superior correlation with physico-chemical properties such as entropy, acentric factor, density and molar volume, outperforming classical indices like the Sombor index, second hyper Zagreb index and redefined third Zagreb index. The second Davan index demonstrates enhanced isomer discrimination capability, as evidenced by its high sensitivity values compared to established descriptors. Further, bounds are established for connected graphs and closed form expressions are computed for standard graph classes and certain nanostructures.