# Cyclic automorphism groups of graphs

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Mariusz Grech

Mathematical Institute Uniwersity of Wrocław

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**Minisymposium:**
GENERAL SESSION TALKS

**Content:**
In 1978 and 1981, S. P. Mohanty, M. R. Sridharan, and S. K. Shukla [2,3] started to consider cyclic automorphism groups, of graphs, of prime and prime power order.
Unfortunately the main results were false or had wrong proofs.
In [1], I gave a full description of cyclic automorphism groups, of graphs and edge-colored graphs, of prime power order.
Now, I will present generalization of this description to all cyclic automorphism groups of graphs and edge-colored graphs.
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\noindent{\bf References:}
\begin{itemize}
\item[{[1]}] M. Grech {\emph Graphical cyclic permutation groups}
Discrete Mathematics 337 (2014), 25–33,
\item[{[2]}] S. P. Mohanty, M. R. Sridharan, S. K. Shukla,
{\emph On cyclic permutation groups and graphs},
J. Math. Phys. Sci. 12 (1978), no. 5, 409--416,
\item[{[3]}] S. P. Mohanty, M. R. Sridharan, S. K. Shukla,
{\emph Graphical cyclic permutation groups},
Combinatorics and graph theory (Calcutta, 1980), 339 -- 346,
Lecture Notes in Math., 885, Springer, Berlin - New York, 1981,
\end{itemize}