STRUCTURE GENERATION FROM A GROSS FORMULA .7. GRAPH ISOMORPHISM - A CONSEQUENCE OF THE VERTEX EQUIVALENCE

The origin of isomorphism in the case of structure generation is examined. It is shown that isomorphism is a consequence of the vertex, hence of bond equivalence. If two equivalent potential extensions are implemented into actual ones in different stages of the generation process, a multiple isomorphism results. A multilevel depth-first procedure for avoiding the generation of duplicated structures is developed. It is based on a two-row matrix representation of the molecular graph. The vertex equivalence is examined at each step of the graph construction, and only non-equivalent extensions are allowed.