$14$-vertex graphs with cyclic automorphism group of order $8$

We describe computational results about undirected graphs having $14$ vertices and automorphism group isomorphic to $\mathbb{Z}\mathrm{/}8\mathbb{Z}$, graphs $\mathrm{\Gamma }$ which have less than $2\mathrm{\mid }Aut(\mathrm{\Gamma })\mathrm{\mid }$ vertices. We give one example of such graphs.