The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic. An important unsolved problem in complexity theory is whether the graph isomorphism problem is in P, NP-complete, or NP-intermediate. The answer is not known, but it is believed that the problem is at least not NP-complete. If graph isomorphism is NP-complete, the polynomial time hierarchy collapses to its second level. Since it is widely believed that the polynomial hierarchy does not collapse to any finite level, it is believed that graph isomorphism is not NP-complete. The best algorithm for this problem, due to Laszlo Babai and Eugene Luks has run time 2O(√(n log(n))) for graphs with n vertices.
What is the problem attributed to defining if two finite graphs are isomorphic? What class is most commonly not ascribed to the graph isomorphism problem in spite of definitive determination? What finite hierarchy implies that the graph isomorphism problem is NP-complete?  To what level would the polynomial time hierarchy collapse if graph isomorphism is NP-complete? Who are commonly associated with the algorithm typically considered the most effective with respect to finite polynomial hierarchy and graph isomorphism?