I was reading the Wikipedia pages on the graph automorphism, but I could not find any solution to the problem (Not even a brute force one). So, is it indeed true that no solutions exist for the general case of the automorphism problem?

P.S. Are there any significant uses of a solution to this problem in pure mathematics, or is the significance of such a solution mostly practical?

Thank you in advance.

  • 4
    $\begingroup$ There's an obvious brute force solution for finite graphs. Are you talking about infinite graphs? $\endgroup$ – Jim Conant Dec 29 '18 at 17:54
  • $\begingroup$ Yes indeed. Is there currently any way to solve the graph automorphism problem in general for infinite graphs? $\endgroup$ – Aryaman Gupta Dec 30 '18 at 4:22

It's not even possible to describe all infinite graphs. The only hope is to restrict to a computable subset. In that case it depends heavily on the subset.


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