Is there an algorithm which will allow me to find an isomorphism between two graphs if I have their adjacency lists?

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The graph isomorphism problem is unusual in that it is NP but probably not NP-complete and no polynomial-time algorithm is known. The Wikipedia article has references for some state-of-the-art algorithms: en.wikipedia.org/wiki/Graph_isomorphism_problem –  joriki Mar 30 '11 at 11:44

As requested, my comment as an answer:

The graph isomorphism problem is unusual in that it is NP but probably not NP-complete and no polynomial-time algorithm is known. The Wikipedia article has references for some state-of-the-art algorithms.

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Even more than that, the graph isomorphism problem is still not even know to be P-complete (even though it most likely is). –  Mitch Mar 30 '11 at 16:36
There is the naive algorithm which tries all permutations of the vertices of 1 graph to map to the other, and then for each permutation, checks if the mapping is an isomorphism. There are $V!$ permutations and checking the mapping takes $O(V+E)$ (why?). So the runtime is exponential.