Isomer Generation: Semantic Rules for Detection of Isomorphism

The problem of exhaustive generation of a nonredundant set of structural formulas (graphs) of acyclic alkanes was considered. A technique based on the compressed adjacency matrix (CAM) was proposed. The algorithm generates CAMs, which encode trees numbered according to the Morgan naming algorithm. Out of this set of CAMs those corresponding to the maximal Morgan codes-which in fact are the CAMs of canonically numbered isomers-must be found. CAMs are conceived as "sentences" of a primitive language. Sentences violating the syntactic and semantic rules of this language have to be discarded. In this paper three semantic rules have been proposed. The algorithm devised is efficient, and the decision to retain or to reject the actual structure does not involve any comparison with other structures. It was proved that several subsets of CAMs will not contain any maximal CAM and therefore it is not necessary to generate them. The whole procedure was illustrated by generating CAMs of all acyclic graphs containing nine vertices.