Read and Corneil dubbed t
Read and Corneil dubbed the study of this problem a "disease." One fast program for handling instances of  this problem is Nauty. One algorithm for solving this problem in the case of restricted multiplicity was given  by Leighton and Miller, and in general it is solved by the Babai-Luks- Zemlyachenko algorithm. One early failed  line of research to solve this problem reduced this problem to eigenvalue spectra and this problem is reducible to Sn  case of the hidden subgroup problem. This problem is in the intersection of NP and coAM. This problem can be  reduced to finding an automorphism group for the object in question. Like factoring, this problem is neither known  to be in P nor NP-complete. For 10 points, name this problem of determining whether there is a 1 to 1 structure  preserving map between two instances of a mathematical structure consisting of nodes and edges.
Read and Corneil dubbed the study of this problem a "disease.
graph isomorphism