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 Γ of square-free order n is one of the following: the lexicographic product \(\sum {[\bar K_b ]}\), or the deleted lexicographic \(\Sigma [\bar K_b ] - b\Sigma \), where n = bm and Σ is an arc-transitive circulant, or Γ is a normal circulant, that is, Aut Γ has a normal regular cyclic subgroup.
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References
B. Alspach, M.D.E. Conder, D. Marušič, and M.Y. Xu, “A classification of 2-arc-transitive circulants,” J. Alg. Combin. 5 (1996), 83-86.
N. Biggs, Algebraic Graph Theory, Cambridge University Press, London, New York, 1992.
J.D. Dixon and B. Mortimer, Permutation Groups, Springer-Verlag, New York, 1996.
C. Godsil, “On the full automorphism group of a graph,” Combinatorica 1 (1981), 243-256.
W. Kantor, “Classification of 2-transitive symmetric designs,” Graphs Combin. 1 (1985), 165-166.
G.O. Sabidussi, “Vertex-transitive graphs,” Monatsh. Math. 68 (1964), 426-438.
M. Suzuki, Group Theory I, Springer-Verlag, Berlin, New York, 1982.
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Li, C., Marušič, D. & Morris, J. Classifying Arc-Transitive Circulants of Square-Free Order. Journal of Algebraic Combinatorics 14, 145–151 (2001). https://doi.org/10.1023/A:1011989913063
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DOI: https://doi.org/10.1023/A:1011989913063