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Graphs and Combinatorics

, Volume 34, Issue 1, pp 241–260 | Cite as

A Complete Classification of Which (nk)-Star Graphs are Cayley Graphs

  • Karimah Sweet
  • Li LiEmail author
  • Eddie Cheng
  • László Lipták
  • Daniel E. Steffy
Original Paper
  • 187 Downloads

Abstract

The (nk)-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 (nk)-star graphs that are Cayley.

Keywords

Interconnection networks Cayley graphs (n k)-star graphs Sabidussi’s Theorem k-homogeneous groups k-transitive groups 

Notes

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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Copyright information

© Springer Japan KK, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsOakland UniversityRochesterUSA

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