TITLE: Build graph with exactly n automorphisms
QUESTION [7 upvotes]: Construct graph with exactly distinct n automorphisms. For n $\geq$ 2.
I wonder if we can just take an asymmetric graph, such as this one as building block.

REPLY [5 votes]: This graph has exactly five automorphisms:

And it's easy to see how to construct a similar graph with $n$ automorphisms for any $n\ge 3$.