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Classifying arc-transitive circulants of square-free order
Li, Caiheng ; Marušič, Dragan ; Morris, Joy
A circulant is a Cayley graph of a cyclic group. Arc-transitive circulants of square-free order are classified. It is shown that an arc-transitive circulant ▫$\Gamma$▫ of square-free order ▫$n$▫ is ...one of the following: the lexicographic product ▫$\Sigma [{\overline K}_b]$▫, or the deleted lexicographic ▫$\Sigma [{\overline K}_b]-b\Sigma$▫, where ▫$n=bm$▫ and ▫$\Sigma$▫ is an arc-transitive circulant, or ▫$\Gamma$▫ is a normal circulant, that is, ▫${\rm Aut}\Gamma$▫ has a normal regular cyclic subgroup.
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