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I am looking for a nice and rigorous proof of Frucht's theorem (every (finite) group is isomorphic to a automorphism group of a (finite) graph). So far, i have looked at the following:

Combinatorial Problems and Exercises by Laszlo Lovasz

Theory of graphs by Oystein Ore

Frucht's original proof (in german)

I was just wondering if someones knows of a nice(r) proof somewhere. I am not quite satisfied with the ones I looked at, I wish some things would be explained more elaborately and rigorously. Both english and german sources would be okay. Thanks in advance!

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  • $\begingroup$ Is there any restriction on the type of graph? That is, are we dealing only with simple (undirected) graphs or with directed graphs as well. $\endgroup$
    – Aurel
    Apr 16, 2018 at 0:01
  • $\begingroup$ For example, if we allow directed multigraphs, this seems to have an extremely simple and elegant proof. $\endgroup$
    – Aurel
    Apr 16, 2018 at 0:03
  • $\begingroup$ Also, have you seen this post? math.stackexchange.com/questions/331207/… $\endgroup$
    – Aurel
    Apr 16, 2018 at 3:27
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    $\begingroup$ I would prefer a version with simple graphs, and yes I have looked at this post. The post together with the book it references is my favourite. I was just hoping that maybe there is an even better version out there somewhere! $\endgroup$
    – Felix R.
    Apr 16, 2018 at 8:50

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