Nonredundant and exhaustive generation of stereoisomers of a chemical compound with a specified constitution is one of the important tools for molecular structure elucidation and molecular design. In this paper, we deal with chemical compounds composed of carbon, hydrogen, oxygen and nitrogen atoms whose graphical structures are tree-like graphs because these compounds are most fundamental, and consider stereoisomers that can be generated by asymmetric carbon atoms and double bonds between two adjacent carbon atoms. Based on dynamic programming, we propose an algorithm of generating all stereoisomers without duplication. We treat a given tree-like graph as a tree rooted at its structural center. Our algorithm first computes recursively the numbers of stereoisomers of the subgraphs induced by the descendants of each vertex, and then constructs each stereoisomer by backtracking the process of computing the numbers of stereoisomers. Our algorithm correctly counts the number of stereoisomers in O(n) time and space, and correctly enumerates all the stereoisomers in O(n) space and in O(n) time per stereoisomer, where n is the number of atoms in a given structure. The source code of the program implementing the proposed algorithm is freely available for academic use upon request.

Exhaustive and nonredundant generating stereoisomers of a chemical compound with a specified constitution is one of the important tools for molecular structure elucidation and molecular design. In this paper we deal with chemical compounds composed of carbon, hydrogen, oxygen and nitrogen atoms whose graphical structures are outerplanar, and consider stereoisomers caused only by asymmetry around carbon atoms. It is known that many chemical compounds have outerplanar graph structures. Based on dynamic programming, we propose an algorithm of generating all stereoisomers without duplication. We treat a given outerplanar graph as a graph rooted at its structural center. Our algorithm first computes recursively the numbers of stereoisomers of the subgraph induced by the descendants of each vertex, and then constructs each stereoisomer by backtracking the process of computing the numbers of stereoisomers. Our algorithm correctly counts the number of stereoisomers in O(n) time and correctly enumerates all the stereoisomers in O(n 3 ) time per stereoisomer on average, where n is the number of atoms in a given structure.

No abstract

Let G be a connected graph in which we designate a vertex or a block (a biconnected component) as the center of G. For each cut-vertex v, let G v be the connected subgraph induced from G by v and the vertices that will be separated from the center by removal of v, where v is designated as the root of G v. We consider the set R of all such rooted subgraphs in G, and assign an integer, called an index, to each of the subgraphs so that two rooted subgraphs in R receive the same indices if and only if they are isomorphic under the constraint that their roots correspond each other. In this paper, assuming a procedure for computing a signature of each graph in a class G of biconnected graphs, we present a framework for computing indices to all rooted subgraphs of a graph G with a center which is composed of biconnected components from G. With this framework, we can find indices to all rooted subgraphs of a outerplanar graph with a center in linear time and space.