A note on the automorphism group of the Hamming graph

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Basic Sciences, Lorestan University, Khorramabad, Iran

Abstract

Let $m>1$ be an integer and $\Omega$ be an $m$-set‎. ‎The Hamming graph $H(n,m)$ has $\Omega ^{n}$ as its vertex-set‎, ‎with two vertices are adjacent if and only if they differ in exactly one coordinate‎. ‎In this paper‎, ‎we provide a new proof on the automorphism group of the Hamming graph $H(n,m)$‎. ‎Although our result is not new (CE Praeger‎, ‎C Schneider‎, ‎Permutation groups and Cartesian decompositions‎, ‎Cambridge University Press‎, ‎2018)‎, ‎we believe that our proof is shorter and more elementary than the known proofs for determining the automorphism group of Hamming graph‎.

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References

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History

  • Receive Date: 29 January 2021
  • Revise Date: 16 February 2021
  • Accept Date: 20 February 2021
  • Published Online: 01 June 2021

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