Novel graphical matrix and distance-based molecular descriptors

We draw attention to graphical matrices as a source of numerous structural invariants that could be used as predictor variables in QSPR and QSAR studies of molecules. In particular, we put forward a novel graphical matrix G associated with a molecule whose off-diagonal element [G](ij) is the subgraph of the corresponding molecular graph obtained from it by deleting vertices i and j. Several molecular descriptors have been extracted from the G matrix and its numerical realization, the G(w) matrix, based on the Wiener index. The usability of the extracted "double" invariants as predictor variables in QSPR studies of molecules has been tested on the total steric energies of octane isomers