An alternative approach to orthogonal graph theoretical invariants

In this work we show that the underlying structure of some graph theoretical invariants used to describe molecular structure, is the vector space Q(root 2, root 3) over the field Q of the rational numbers. On Q(root 2, root 3) we define a symmetric bilinear form and then proceed to use the Gram-Schmidt orthogonalization process. In this way we formalize Randic's idea of orthogonalizing molecular descriptors which is based on residuals of stepwise multiple regression analysis, since the results presented here make it possible to obtain a basis of graph theoretical invariants.