We have developed an algorithm for exhaustively enumerating all plausible AAM solutions based on the MCESs in chemical reactions. Our framework incorporates an enumeration algorithm to identify all possible maximum cliques by SA-based Ising computing. This enumeration algorithm not only accurately identifies the maximum cliques corresponding to the MCESs but also significantly outperforms established exact algorithms for maximum clique enumeration in terms of computational time. Furthermore, our proposed AAM algorithm surpasses existing AAM tools in terms of chemical correctness. Additionally, it identifies multiple nonequivalent mappings in some cases, and these enumerated mappings include chemically correct reaction patterns. This advancement provides a valuable tool for chemoinformatics, enabling more precise and efficient investigations of reaction mechanisms in organic chemistry.