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 (Skiena 1990, p. 181), and as a result, the problem is sometimes assigned to a special graph isomorphism complete complexity class.
Graph Isomorphism Complete
See also
Complexity Theory, Graph Isomorphism, Isomorphic Graphs, NP-Complete Problem, P-ProblemExplore with Wolfram|Alpha
References
Garey, M. R. and Johnson, D. S. Computers and Intractability: A Guide to the Theory of NP-Completeness. New York: W. H. Freeman, pp. 155-156, 1983.Skiena, S. "Graph Isomorphism." §5.2 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 181-187, 1990.Referenced on Wolfram|Alpha
Graph Isomorphism CompleteCite this as:
Weisstein, Eric W. "Graph Isomorphism Complete." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GraphIsomorphismComplete.html