Abstract
The (n, k)-star graphs are an important class of interconnection networks that generalize star graphs, which are superior to hypercubes. In this paper, we continue the work begun by Cheng et al. (Graphs Combin 33(1):85–102, 2017) and complete the classification of all the (n, k)-star graphs that are Cayley.
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Notes
Even though this minimum condition on r is not stated in [11, Theorem 5.2B], a Remark after Theorem 5.2B mentions that “the group are listed only with the minimum r for which they satisfy the hypotheses of the theorem”. Without the minimum condition, there could be more exceptional cases such as (6, 3, 6), (6, 3, 12), (8, 4, 30).
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Acknowledgements
We are grateful to the anonymous referees for carefully reading through the manuscript and giving us many constructive suggestions to improve the presentation. We would also like to thank P. Ingram, J. Silverman, and T. Tucker for their helpful comments on primitive divisors and Zsigmondy sets. Magma Computational Algebra System [3] did many computations that are essential to our project.
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The second author was partially supported by the Oakland University URC Faculty Research Fellowship Award.
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Sweet, K., Li, L., Cheng, E. et al. A Complete Classification of Which (n, k)-Star Graphs are Cayley Graphs. Graphs and Combinatorics 34, 241–260 (2018). https://doi.org/10.1007/s00373-017-1871-7
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DOI: https://doi.org/10.1007/s00373-017-1871-7