On the Cayley graphs of symmetric group $S_4$

Document Type : Research Paper

Author

Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran

Abstract

Let $S_n$ be the symmetric group of degree $n$. In this paper, we classify non-isomorphic Cayley graphs of $S_4$ of valency 3. Moreover, we verify that there are exactly 10 non-isomorphic  Cayley graphs of $S_4$ with valency 3. Also, we classify  the valency 3 CI-graphs of    Cayley graphs of  $S_4$ and  we prove that $S_4$ is not a CI-group and does not possess the $3$-CI-property. We show that  there are at least 10 non-isomorphic Cayley graphs of the symmetric group $S_n$ with valency 3.

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References

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History

  • Receive Date: 07 November 2024
  • Revise Date: 09 April 2025
  • Accept Date: 09 May 2025

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