The Graph Isomorphism Problem

Exploring the theoretical and practical aspects of the graph isomorphism (GI) problem is essential to find a solution. Deciding whether two graphs are structurally identical, or isomorphic, is a classical algorithmic problem that has been studied by many researchers. Applications span a broad field of areas ranging from chemistry to computer vision. Closely related is the problem of detecting symmetries of graphs and of general combinatorial structures. This has many application domains, for example, combinatorial optimization, the generation of combinatorial structures, and the computation of normal forms. With its many practical and theoretical applications the GI problem remains one of the most important unresolved problems in theoretical computer science. A recent breakthrough by LaÁszloÁ Babai shows that the problem is almost efficiently solvable theoretically.