  Theoretical molecular descriptors alias topological indices are a convenient
means for expressing in a numerical form the chemical structure encoded in a
molecular graph. The structure descriptors derived from molecular graphs are
widely used in Quantitative Structure-Property Relationship (QSPR) and
Quantitative Structure-Activity Relationship (QSAR).
  In this paper, we are interested in the Graovac-Pisanski index (also called
modified Wiener index) introduced in 1991 by Graovac and Pisanski, which
encounters beside the distances in a molecular graph also its symmetries. In
the QSPR analysis we first calculate the Graovac-Pisanski index for different
families of hydrocarbon molecules using a simple program and then we show a
correlation with the melting points of considered molecules. We show that the
melting points of the alkane series can be very effectively predicted by the
Graovac-Pisanski index and for the rest of considered molecules (PAH's and
octane isomers) the regression models are different, but we establish some
correlation with the melting points for them as well.
