Asymetric graph with three nods

  1. Why isn't this graph:
    1-2 3
    asymetric?
    I think there exists only one automorphism:
    2-1 3
    but I'm also supposed to prove that ther are no asymetric graphs with 1<|V(G)|<=5
    so it can't be assymetric
     
  2. jcsd
  3. Oh I see now! It can have no non-trivial symmetries and permutation (1 2) is already a non-trivial symmetry.
    Sorry to bother
     
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