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

Enumerating Chemical Graphs with Two Disjoint Cycles Satisfying Given Path Frequency Specifications