# Article

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Keywords:
graph; automorphism group
Summary:
The problem of finding minimal vertex number of graphs with a given automorphism group is addressed in this article for the case of cyclic groups. This problem was considered earlier by other authors. We give a construction of an undirected graph having \$4n+6\$ vertices and automorphism group cyclic of order \$4n\$, \$n\ge 1\$. As a special case we get graphs with \$2^k+6\$ vertices and cyclic automorphism groups of order \$2^k\$. It can revive interest in related problems.
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