# A note on another construction of graphs with $4n+6$ vertices and cyclic automorphism group of order $4n$

## Peteris Daugulis

Address: Institute of Life Sciences and Technologies, Daugavpils University, Daugavpils, LV-5400, Latvia

E-mail: peteris.daugulis@du.lv

Abstract: 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.

AMSclassification: primary 05C25; secondary 05E18, 05C35, 05C75.

Keywords: graph, automorphism group.

DOI: 10.5817/AM2017-1-13