Enumerating Chemical Graphs of 1-Tree Structure from Given Upper and Lower Bounds on Path Frequencies

Abstract

Enumeration of chemical graphs (molecular graphs) satisfying given constraints is one of the fundamental problems in chemoinformatics and bioinformatics since it leads to a variety of useful applications including structure determination of novel chemical compounds and drug design. We consider the problem of enumerating chemical graphs of monocyclic structure (a graph structure that contains exactly one cycle) from a given set of feature vectors which is specified by a pair of upper and lower feature vectors, where a feature vector represents frequency of prescribed paths in a chemical compound to be constructed. To enumerate all tree-like (acyclic) chemical graphs from a given set of feature vectors, Shimizu et al. and Suzuki et al. have already proposed efficient branch-and-bound algorithms based on a fast tree enumeration algorithm. In this study, we devise a novel method for extending the efficient algorithms of enumerating tree-like chemical graphs to enumeration of chemical graphs of monocyclic structure by designing a fast algorithm for testing canonicality of monocyclic structures.