Classifying Arc-Transitive Circulants of Square-Free Order
Caiheng Li
, Dragan Marušič
and Joy Morris
DOI: 10.1023/A:1011989913063
Abstract
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 å[[ `( K)] b ] \sum {[\bar K_b ]} , or the deleted lexicographic S[[ `( K)] b ] - b S Σ[\bar K_b ] - bΣ , where n = bm and 
is an arc-transitive circulant, or 
is a normal circulant, that is, Aut has a normal regular cyclic subgroup.
is an arc-transitive circulant, or is a normal circulant, that is, Aut has a normal regular cyclic subgroup.Pages: 145–151
Keywords: circulant graph; arc-transitive graph; square-free order; cyclic group; primitive group; imprimitive group
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7. M. Suzuki, Group Theory I, Springer-Verlag, Berlin, New York, 1982.