We describe computational results about undirected graphs having $14$ vertices and automorphism group isomorphic to $\mathbb{Z}/8\mathbb{Z}$, graphs $\Gamma$ which have less than $2|Aut(\Gamma)|$ vertices. We give one example of such graphs.
$10$-vertex graphs with cyclic automorphism group of order $4$
Graphs with $2^n+6$ vertices and cyclic automorphism group of order $2^n$
Exponentially many graphs are determined by their spectrum
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