AUTOMORPHISM AND EQUIVALENCE CLASSES

Previously described determinations of equivalence classes of atoms in molecules have been based upon the use of graph invariants. Because invariants do not adequately convey all of the information present in a connection table, more or less complicated methods of refinement must be applied to compensate. A method for finding equivalence classes is presented that is theoretically complete because it is based on all possible mappings of a graph onto itself This method, usually considered to be computationally impractical, is in fact a useful approach to the determination of topological symmetry. The procedure uses preliminary processing based on a few graph invariants and the Morgan algorithm to induce an initial partition, which markedly accelerates subsequent mappings of a graph onto itself. As new symmetries are discovered, they are used to induce new partitions, which accelerates the process even more. In recalcitrant cases, where the usual graph invariants of atom identity and bond distribution are not sufficient to induce partitioning, the determination of ring membership may be useful.