On Reconstruction of Normal Edge-Transitive Cayley Graphs

Abstract

The main idea of this paper is to provide an algebraic algorithm for constructing symmetric graphs with optimal fault tolerance. For this purpose, we use normal edge-transitive Cayley graphs and the idea of reconstruction question posed by Praeger to present a special factorization of groups which induces a graphical decomposition of normal edge-transitive Cayley graphs to simpler normal edge-transitive Cayley graphs. Then as a consequence of our results, we continue the study of normal edge-transitive Cayley graphs of abelian groups and we show that knowing normal edge-transitive Cayley graphs of abelian p-groups, we can determine all normal edge-transitive Cayley graphs of abelian groups.

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Acknowledgements

The authors would like to express their gratitude to the referee for very valuable suggestions, which improved the manuscript and the proofs of Theorems 1.3 and 1.4, essentially.

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Correspondence to Behnam Khosravi.

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Khosravi, B., Khosravi, B. & Khosravi, B. On Reconstruction of Normal Edge-Transitive Cayley Graphs. Ann. Comb. (2020). https://doi.org/10.1007/s00026-020-00514-3

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Mathematics Subject Classification

  • Primary 05C25
  • Secondary 08A30
  • 08A35

Keywords

  • Normal edge-transitive Cayley graphs
  • Factorization of groups
  • Optimal fault tolerance