Let call a simple graph (not containing neither loops, nor multiple edges) "prime", if it has no non-trivial automorphisms, i.e. graph that has only "identity" automorphic transformation. I cannot find an example of prime graphs. Do they exist?



A question about graphs not having non-trivial automorphisms
Frucht's theorem states that every finite group is the group of automorphisms of a finite undirected graph. The Frucht graph, is a $3$-regular graph whose automorphism group is the trivial group.


See <http://en.wikipedia.org/wiki/Frucht%27s_theorem>


