Number of nodes in cubic graphs with no non-trivial automorphisms Is there some sort of characterization of all such numbers $n$, that there exists a cubic graph with $2n$ vertices and no non-trivial automorphisms. Frucht theorem states, that any finite group is an automorphism group of some cubic groups. In particular case, the minimal cubic graph with trivial automorphism group is called Frucht graph and has $12$ vertices. However, I do not know, of what size can the larger examples be...

The paper < claims to construct an explicit example for every even $n$ at least 12. (See Section 3.)

I don't think this paper has appeared yet, so caveat emptor.