Graphs with 2ⁿ+6 vertices and cyclic automorphism group of order 2ⁿ

الأصل · EN

The problem of finding upper bounds for minimal vertex number of graphs with a given automorphism group is addressed in this article for the case of cyclic 2-groups. We show that for any natural n≥ 2 there is an undirected graph having 2ⁿ+6 vertices and automorphism group cyclic of order 2ⁿ. This confirms an upper bound claimed by other authors for minimal number of vertices of undirected graphs having automorphism group Z/2ⁿZ.