The simple graphs upto $11$ vertices do not have $5,7,9,...$ automorphisms, in other words, the only odd numbers appearing are $1$ and $3$. Is this true for all graphs ?
Formulated as an existence-question :
Is there an odd number $k\ge 5$ and a simple graph G with $|Aut(G)|=k$?
In particular, is there a simple graph with $5$ automorphisms ?