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I am doing some literature review on Graph isomorphism problem. Most of papers which I am reading are written by E.M Luks and Laszlo Babai. These papers uses the high level knowledge of group theory and complexity theory. As I am new to this field many of the things are not clear to me.

Can some one suggest me a way to learn ideas and techniques which are presented in these papers so that I can come up with some other ideas.

Thank you so much

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I highly recommend Paolo Codenotti's thesis for the group-theoretic aspects, and the book The Graph Isomorphism Problem: Its Structural Complexity by Johannes Köbler, Uwe Schöning, and Jacobo Torán for the complexity aspects.

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http://oeis.org/A186202 is the best you can do for automorphism by brute force permutation checking.

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