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Diskr. Mat., 2018, Volume 30, Issue 4, Pages 66–87 (Mi dm1487)  

Классификация дистанционно транзитивных графов орбиталов надгрупп группы Джевонса

B. A. Pogorelova, M. A. Pudovkinab

a Academy of Cryptography of Russian Federation
b Bauman Moscow State Technical University

Abstract: The Jevons group $A{\tilde S_n}$ is an isometry group of the Hamming metric $\chi_{n}$ on the $n$-dimensional vector space ${V_n}$ over $GF(2)$. It is generated by the group of all permutation $(n \times n)$-matrices over $GF(2)$ and the translation group on ${V_n}$. In [3], [4], [5], we classified submetrics of $\chi_{n}$ and all overgroups of $A{\tilde S_n}$, which are isometry groups of the submetrics of $\chi_{n}$. Moreover, each overgroup of $A{\tilde S_n}$ defines orbital graphs whose metrics are submetrics of $\chi_{n}$. In [6], we described all distance-transitive orbital graphs of overgroups of $A{\tilde S_n}$. In this paper, these distance-transitive orbital graphs are corresponded to well-known classes of graphs. In particular, we show that some distance-transitive orbital graphs are isomorphic to the following classes: the complete graph ${K_{{2^n}}}$, the complete bipartite graph ${K_{{2^{n - 1}}{{,2}^{n - 1}}}}$, the halved $(n + 1)$-cube, the folded $(n + 1)$-cube, alternating forms graphs, the Taylor graph, the Hadamard graph, incidence graphs of square designs.

Keywords: orbital graph, Jevons group, distance-transitive graph, Hamming graph, Taylor graph, Hadamard graph.

DOI: https://doi.org/10.4213/dm1487

Full text: PDF file (275 kB)
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Document Type: Article
UDC: 519.172+512.542.7
Received: 28.11.2017

Citation: B. A. Pogorelov, M. A. Pudovkina, “Классификация дистанционно транзитивных графов орбиталов надгрупп группы Джевонса”, Diskr. Mat., 30:4 (2018), 66–87

Citation in format AMSBIB
\Bibitem{PogPud18}
\by B.~A.~Pogorelov, M.~A.~Pudovkina
\paper Классификация дистанционно транзитивных графов орбиталов надгрупп группы Джевонса
\jour Diskr. Mat.
\yr 2018
\vol 30
\issue 4
\pages 66--87
\mathnet{http://mi.mathnet.ru/dm1487}
\crossref{https://doi.org/10.4213/dm1487}
\elib{http://elibrary.ru/item.asp?id=36447993}


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