The Frucht graph is one of the two smallest cubic graphs possessing only a single graph automorphism, the identity (that is, every vertex can be distinguished topologically from every other vertex).
What exactly is meant by saying that there are two, and what is the other one?
I assume it doesn't simply mean that there are two non-isomorphic ones because with a small computational experiment, I seem to find 5 different asymmetric cubic graphs on 12 vertices. Of these 5, the last one is the Frucht graph.
In graph6 notation,
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