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We consider a problem of enumerating chemical graphs from given constraintsconcerning their structures, which has an important application to a novelmethod for the inverse QSAR/QSPR recently proposed. In this paper, thestructure of a chemical graph is specified by a feature vector each of whoseentries represents the frequency of a prescribed path. We call a graph a2-augmented tree if it is obtained from a tree (an acyclic graph) by addingedges between two pairs of nonadjacent vertices. Given a set of feature vectorsas the interval between upper and lower bounds of feature vectors, we design anefficient algorithm for enumerating chemical 2-augmented trees that satisfy thepath frequency specified by some feature vector in the set. We implemented theproposed algorithm and conducted some computational experiments.

Enumerating Chemical Graphs with Mono-block 2-Augmented Tree Structure from Given Upper and Lower Bounds on Path Frequencies