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

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Abstract

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 \({\cal P}{\cal N}{\cal C}\).

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Authors and Affiliations

  1. Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA

    Ákos Seress

  2. Department of Mathematics and Statistics, The University of Western Australia, Perth, 6907, WA, Australia

    Ákos Seress

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  1. Ákos Seress
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Seress, Á. Square-Free Non-Cayley Numbers. On Vertex-Transitive Non-Cayley Graphs of Square-Free Order. Des Codes Crypt 34, 265–281 (2005). https://doi.org/10.1007/s10623-004-4859-2

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