DETERMINATION OF TOPOLOGICAL EQUIVALENCE IN MOLECULAR GRAPHS FROM THE TOPOLOGICAL STATE

A method for computer perception of topological equivalence is presented along with consequences for analysis of molecular graphs and applications to SAR. This method is based on a new concept called the topological state of skeletal atoms. Topological equivalence is the molecular characteristic associated with structure equivalences within the molecular skeleton without regard to full three‐dimensional geometry. In this investigation, structure is represented by the chemical graph (hydrogen‐suppressed graph). Topological equivalence, the equivalence of skeletal atoms, is based upon numerical equality of the topological state values introduced in this method. The topological state value for an atom is defined in terms of three quantities: the number of skeletal paths terminating on that atom, the number of atoms in each path (graph separation), and a numerical expression for the chemical identity of each atom. Atom identity is encoded by the molecular connectivity valence delta value. Several algorithms for computation of topological state value are examined, all based on use of the geometric mean of the valence delta values of the atoms in each path. It is shown for a large number of molecules with a wide variety of structure types that proper topological equivalence perception is achieved by this method for several algorithm formulations. This formalism of topological state may prove highly useful as a characterization of the environment of skeletal atoms. The total topological index also introduced here appears to be a highly discriminating index of molecular graphs. Implications for structure‐activity studies are discussed and two example QSAR uses of the total topological index are presented: gas chromatographic retention index for alcohols and inhibition of T. mentagrohpytes by phenylpropylethers. Copyright © 1990 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim