Discrete Mathematics & Theoretical Computer Science,Vol 16, No 2

摘要

The graph isomorphism (GI) problem asks whether two given graphs areisomorphic or not. The GI problem is quite basic and simple, however,it's time complexity is a long standing open problem. The GI problemis clearly in NP, no polynomial time algorithm is known, and the GIproblem is not NP-complete unless the polynomial hierarchy collapses.In this paper, we survey the computational complexity of the problemon some graph classes that have geometric characterizations.Sometimes the GI problem becomes polynomial time solvable when we addsome restrictions on some graph classes. The properties of thesegraph classes on the boundary indicate us the essence of difficulty ofthe GI problem. We also show that the GI problem is as hard as theproblem on general graphs even for grid unit intersection graphs on atorus, that partially solves an open problem.