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automorphism of a graph

I was wondering if someone could help me determine whether a graph admits a semiregular automorphism, based on the following definition.

A non-identity automorphism of a graph is semiregular, in particular, $(k, n)$-semiregular if it has $k$ cycles of equal length $n$ in its cycle decomposition.

Thank you so much.

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automorphism of a graph

I was wondering if someone could help me determine whether a graph admits a semiregular automorphism, based on the following definition.

A non-identity automorphism of a graph is semiregular, in particular, $(k, n)$-semiregular if it has $k$ cycles of equal length $n$ in its cycle decomposition.

Thank you so much.