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A note on the automorphism group of the Hamming graph | ||
| Transactions on Combinatorics | ||
| دوره 10، شماره 2، شهریور 2021، صفحه 129-136 اصل مقاله (426 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2021.127225.1817 | ||
| نویسندگان | ||
| Seyed Morteza Mirafzal* ؛ Meysam Ziaee | ||
| Department of Mathematics, Faculty of Basic Sciences, Lorestan University, Khorramabad, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| automorphism group؛ Hamming graph؛ vertex-transitive graph؛ wreath product | ||
| مراجع | ||
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[14] S. M. Mirafzal, More odd graph theory from another point of view, Discrete Math., 341 (2018) 217–220.
[15] S. M. Mirafzal and M. Ziaee, Some algebraic aspects of enhanced Johnson graphs, Acta Math. Univ. Comenianae, 88 (2019) 257–266. [16] S. M. Mirafzal, The automorphism group of the bipartite Kneser graph, Proc. Indian Acad. Sci. Math. Sci., 129 no. 3 (2019) 8 pp. [17] S. M. Mirafzal, Cayley properties of the line graphs induced by consecutive layers of the hypercube, Bull. Malays. Math. Sci. Soc., 44 (2021) no. 3 1309–1326. [18] S. M. Mirafzal, On the automorphism groups of connected bipartite irreducible graphs, Proc. Indian Acad. Sci. Math. Sci., 130 (2020) no. 1 15 pp. [19] S. M. Mirafzal, On the distance-transitivity of the square graph of the hypercube, arXiv: 2101.01615v2 (2021).
[20] C. E. Praeger and C. Schneider, Permutation groups and Cartesian decompositions, Cambridge University Press, 2018. [21] J. X. Zhou, The automorphism group of the alternating group graph, Appl. Math. Lett., 24 (2011) 229–231. | ||
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