The Method of Ideal Symmetry is applied to define new 3D and 4D molecular descriptors on the basis of some analogies with the vertex distance sum in molecular graphs, These new descriptors are employed together with well-known topological descriptors to make up a pool of available variables to perform a multilinear regression analysis of alkanes normal boiling points. Predictions are satisfactory and they compare fairly well with other available theoretical data. The fitting polynomials are improved through the analysis of nonlinear models and in such cases predictions are ameliorated, although not in a very spectacular manner. Finally, some possible extensions of the present study are pointed out. (C) 2002 Published by Elsevier Science B.V.