Designs, Codes and Cryptography

, Volume 34, Issue 2–3, pp 265–281 | Cite as

Square-Free Non-Cayley Numbers. On Vertex-Transitive Non-Cayley Graphs of Square-Free Order

  • Ákos SeressEmail author


A complete classification is given of finite primitive permutation groups which contain a regular subgroup of square-free order. Then a collection \({\cal P}{\cal N}{\cal C}\) of square-free numbers n is obtained such that there exists a vertex-primitive non-Cayley graph on n vertices if and only if n is a member of \({\cal P}{\cal N}{\cal C}\).


Data Structure Information Theory Discrete Geometry Permutation Group Complete Classification 
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© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of MathematicsThe Ohio State UniversityColumbusUSA
  2. 2.Department of Mathematics and StatisticsThe University of Western AustraliaPerthAustralia

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