  Enumerating chemical graphs satisfying given constraints is a fundamental
problem in mathematical and computational chemistry, and plays an essential
part in a recently proposed framework for the inverse QSAR/QSPR. In this paper,
constraints are given by feature vectors each of which consists of the
frequencies of paths in a given set of paths. We consider the problem of
enumerating chemical graphs that satisfy the path frequency constraints, which
are given by a pair of feature vectors specifying upper and lower bounds of the
frequency of each path. We design a branch-and-bound algorithm for enumerating
chemical graphs of bi-block 2-augmented structure, that is, graphs that contain
two edge-disjoint cycles. We present some computational experiments with an
implementation of our proposed algorithm.
