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-Problem## Explore 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 Complete## Cite this as:

Weisstein, Eric W. "Graph Isomorphism Complete."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/GraphIsomorphismComplete.html