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Constructing 2-Arc-Transitive Covers of Hypercubes

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Abstract

We introduce the notion of a symmetric basis of a vector space equipped with a quadratic form, and provide a sufficient and necessary condition for the existence to such a basis. Symmetric bases are then used to study Cayley graphs of certain extraspecial 2-groups of order \(2^{2r+1}\) (\(r\ge 1\)), which are further shown to be normal Cayley graphs and 2-arc-transitive covers of 2r-dimensional hypercubes.

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Acknowledgements

This research is part of my Ph.D project at the Centre for the Mathematics of Symmetry and Computation of the University of Western Australia. I would like to express my gratitude to my supervisors Dr. Michael Giudici and Dr. Caiheng Li, who offered continuous advice and encouragement throughout the progress of this paper. I would also like to thank the referees of this paper for their great suggestions, which helped me a lot in improving the presentation of this paper.

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Authors and Affiliations

  1. Centre for the Mathematics of Symmetry and Computation, School of Mathematics and Statistics, The University of Western Australia, Crawley, Australia

    Michael Giudici

  2. Department of Mathematics, Southern University of Science and Technology, Shenzhen, China

    Caiheng Li

  3. School of Mathematics, Southeast University, Nanjing, China

    Yian Xu

Authors
  1. Michael Giudici
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  2. Caiheng Li
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  3. Yian Xu
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Correspondence to Yian Xu.

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Giudici, M., Li, C. & Xu, Y. Constructing 2-Arc-Transitive Covers of Hypercubes. Graphs and Combinatorics 35, 973–987 (2019). https://doi.org/10.1007/s00373-019-02049-8

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  • DOI: https://doi.org/10.1007/s00373-019-02049-8

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