A note on the automorphism group of the Hamming graph
Publish place: Transactions on Combinatorics، Vol: 10، Issue: 2
Publish Year: 1400
نوع سند: مقاله ژورنالی
زبان: English
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تاریخ نمایه سازی: 14 اردیبهشت 1400
Abstract:
Let $m>۱$ 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, ۲۰۱۸), 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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Authors
Seyed Morteza Mirafzal
Department of Mathematics, Faculty of Basic Sciences, Lorestan University, Khorramabad, Iran
Meysam Ziaee
Department of Mathematics, Faculty of Basic Sciences, Lorestan University, Khorramabad, Iran