  We consider a problem of enumerating chemical graphs from given constraints
concerning their structures, which has an important application to a novel
method for the inverse QSAR/QSPR recently proposed. In this paper, the
structure of a chemical graph is specified by a feature vector each of whose
entries represents the frequency of a prescribed path. We call a graph a
2-augmented tree if it is obtained from a tree (an acyclic graph) by adding
edges between two pairs of nonadjacent vertices. Given a set of feature vectors
as the interval between upper and lower bounds of feature vectors, we design an
efficient algorithm for enumerating chemical 2-augmented trees that satisfy the
path frequency specified by some feature vector in the set. We implemented the
proposed algorithm and conducted some computational experiments.
