There exists no known P algorithm for graph isomorphism testing, although the problem has also not been shown to be NP-complete. In fact, the problem of identifying isomorphic graphs seems to fall in a crack between P and NP-complete, if such a crack exists, and as a result, the problem is sometimes assigned to a special graph isomorphism complete complexity class.

complexity theory | graph isomorphism | isomorphic graphs | NP-complete problem | P-problem