A note on the automorphism group of the Hamming graph
نویسندگان
1 Department of Mathematics, Faculty of Basic Sciences, Lorestan University, Khorramabad, Iran
2 Department of Mathematics, Faculty of Basic Sciences, Lorestan University, Khorramabad, Iran
doi
10.22108/toc.2021.127225.1817چکیده
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.
