We propose an AAM algorithm that enumerates all plausible mappings without reaction rules. We formulate the AAM problem as maximum common edge subgraph (MCES) problem, which corresponds to finding atom label mapping(s) that minimize the number of bond cleavages and formations. The MCES problem is then reduced to the maximum clique problem, i.e., finding the largest subgraph(s) where all nodes are fully connected to each other. To solve the maximum clique problem, our proposed framework employs an enumeration algorithm utilizing Ising computing. Ising computing is a novel paradigm that has gained significant attention as an efficient approach for solving hard combinatorial optimization problems across various fields, including chemistry. Finally, candidate mappings are constructed from the MCESs computed using Ising computing and are then clustered into distinct reaction patterns through a symmetry reduction method. We elaborate on our proposed algorithm in Section 2.