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Cayley graphs on abelian groups

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Abstract

Let A be an abelian group and let ι be the automorphism of A defined by: ι: a ↦ a−1. A Cayley graph Γ = Cay(A,S) is said to have an automorphism group as small as possible if Aut(Γ)=A⋊<ι>. In this paper, we show that almost all Cayley graphs on abelian groups have automorphism group as small as possible, proving a conjecture of Babai and Godsil.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Mississippi State University, PO Drawer MA, Starkville, Mississippi State, MS 39762, USA

    Edward Dobson

  2. Inštitut Andrej Marušic, University of Primorska, Koper, Slovenia, 6000, USA

    Edward Dobson

  3. Departimento di Matematica Pura e Applicata, University of Milano-Bicocca, 20126, Milano, Italy

    Pablo Spiga

  4. Centre for Mathematics of Symmetry and Computation, School of Mathematics and Statistics, The University of Western Australia, Crawley, WA, 6009, Australia

    Gabriel Verret

  5. University of Primorska, FAMNIT, 6000, Koper, Slovenia

    Gabriel Verret

Authors
  1. Edward Dobson
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  2. Pablo Spiga
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  3. Gabriel Verret
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Corresponding author

Correspondence to Gabriel Verret.

Additional information

The third author is supported by UWA as part of the Australian Research Council grant DE130101001.

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Dobson, E., Spiga, P. & Verret, G. Cayley graphs on abelian groups. Combinatorica 36, 371–393 (2016). https://doi.org/10.1007/s00493-015-3136-5

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  • DOI: https://doi.org/10.1007/s00493-015-3136-5

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