Abstract: This report systematically reviews a series of research efforts aimed at tackling the Graph Reconstruction Conjecture. The research began with the construction of Multiset Space (MS) theory, which was progressively developed into a core framework for studying graph isomorphism and reconstruction problems. We outline the evolution of this theory from its foundational concepts to its unification with topological notions, and detail the two main instrumental branches derived from it for attacking the conjecture: Orbit Fingerprint Theory and the Functional Algebraic Analysis approach. Although the direct assault on the original conjecture was not fully successful, several significant theoretical achievements were made during this process, including proving the reconstructibility of rigid asymmetric graphs, establishing Multiset Space as a complete invariant for graph isomorphism, and ultimately fostering a more general systematic research framework. This review aims to elucidate the internal logic, key contributions, and lessons learned from this series of works to inform future research.
Jianming Wang (Fri,) studied this question.