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Sibirsk. Mat. Zh., 2013, Volume 54, Number 6, Pages 1353–1367 (Mi smj2501)  

This article is cited in 5 scientific papers (total in 5 papers)

Edge-symmetric distance-regular coverings of cliques: The affine case

A. A. Makhnev, D. V. Paduchikh, L. Yu. Tsiovkina

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia

Abstract: Let $\Gamma$ be an edge-symmetric distance-regular covering of a clique. Then the group $G=\mathrm{Aut}(\Gamma)$ acts twice transitively on the set $\Sigma$ of antipodal classes. We propose a classification for the graphs based on the description of twice transitive permutation groups. This program is realized for $a_1=c_2$. In this article we classify graphs in the case when the action of $G$ on $\Sigma$ is affine.

Keywords: distance-regular graph, edge-symmetric graph, automorphism group.

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English version:
Siberian Mathematical Journal, 2013, 54:6, 1076–1087

Bibliographic databases:

UDC: 519.17+512.54
Received: 29.10.2012
Revised: 20.02.2013

Citation: A. A. Makhnev, D. V. Paduchikh, L. Yu. Tsiovkina, “Edge-symmetric distance-regular coverings of cliques: The affine case”, Sibirsk. Mat. Zh., 54:6 (2013), 1353–1367; Siberian Math. J., 54:6 (2013), 1076–1087

Citation in format AMSBIB
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\by A.~A.~Makhnev, D.~V.~Paduchikh, L.~Yu.~Tsiovkina
\paper Edge-symmetric distance-regular coverings of cliques: The affine case
\jour Sibirsk. Mat. Zh.
\yr 2013
\vol 54
\issue 6
\pages 1353--1367
\mathnet{http://mi.mathnet.ru/smj2501}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3184100}
\transl
\jour Siberian Math. J.
\yr 2013
\vol 54
\issue 6
\pages 1076--1087
\crossref{https://doi.org/10.1134/S0037446613060141}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84891341821}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. Yu. Tsiovkina, “On automorphisms of a distance-regular graph with intersection array $\{35,32,1;1,4,35\}$”, Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), 209–215  mathnet  crossref  mathscinet  isi  elib
    2. L. Yu. Tsiovkina, “Ob affinnykh distantsionno regulyarnykh nakrytiyakh polnykh grafov”, Sib. elektron. matem. izv., 12 (2015), 998–1005  mathnet  crossref
    3. L. Yu. Tsiovkina, “Arc-transitive antipodal distance-regular covers of complete graphs related to $SU_3(q)$”, Discrete Math., 340:2 (2017), 63–71  crossref  mathscinet  zmath  isi  scopus
    4. A. A. Makhnev, M. P. Golubyatnikov, “Avtomorfizmy distantsionno regulyarnogo grafa s massivom peresechenii $\{63,60,1; 1,4,63\}$”, Sib. elektron. matem. izv., 14 (2017), 1064–1077  mathnet  crossref
    5. A. A. Makhnev, D. V. Paduchikh, L. Yu. Tsiovkina, “Edge-symmetric distance-regular coverings of complete graphs: the almost simple case”, Algebra and Logic, 57:2 (2018), 141–152  mathnet  crossref  crossref  isi
  • Сибирский математический журнал Siberian Mathematical Journal
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