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I would like a good hint for the following problem that takes into account the position at which I am stuck. The problem is as follows

Let $\mathbb{Z}_n$ be the cyclic group of order $n.$ Find a simple graph $G$ such that $\mathrm{Aut}(G) = \mathbb{Z}_n.$

The book that I am studying suggest that somehow I get rid of the "unwanted" symmetries of the cycle graph $C_n.$ We know that $\mathrm{Aut}(C_n) = D_{2n}$ and somehow we would like to "kill" the "reflections" of $C_n.$ I don't see any way how to "kill" the reflections while "preserving" the rotational symmetries of $C_n.$

Any hint would be appreciated!

  • 0
    Are the graphs allowed to be directed?2012-12-18
  • 0
    No the graphs are simple!2012-12-18

2 Answers 2