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Algebra Logika, 2017, Volume 56, Number 4, Pages 395–405 (Mi al804)  

This article is cited in 1 scientific paper (total in 1 paper)

Automorphism groups of small distance-regular graphs

I. N. Belousov, A. A. Makhnev

Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990 Russia

Abstract: We consider undirected graphs without loops and multiple edges. Previously, V. P. Burichenko and A. A. Makhnev [Modern Problems in Mathematics: Proc. 42nd All-Russian SchoolConference of Young Scientists, Yekaterinburg, Institute of Mathematics and Mechanics, UB RAS, 2011, 181–183] found intersection arrays of distance-regular locally cyclic graphs with the number of vertices at most 1000. It is shown that the automorphism group of a graph with intersection array $\{15,12,1;1,2,15\}$, $\{35,32,1;1,2,35\}$, $\{39,36,1;1,2,39\}$ or $\{42,39,1;1,3,42\}$ (such a graph enters the above-mentioned list) acts intransitively on the set of its vertices.

Keywords: distance-regular graph, locally cyclic graph, intersection array, automorphism group.

Funding Agency Grant Number
Russian Science Foundation 14-11-00061
Supported by Russian Science Foundation, project No. 14-11-00061.


DOI: https://doi.org/10.17377/alglog.2017.56.401

Full text: PDF file (160 kB)
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English version:
Algebra and Logic, 2017, 56:4, 261–268

Bibliographic databases:

UDC: 519.17+512.54
Received: 27.02.2015
Revised: 29.09.2016

Citation: I. N. Belousov, A. A. Makhnev, “Automorphism groups of small distance-regular graphs”, Algebra Logika, 56:4 (2017), 395–405; Algebra and Logic, 56:4 (2017), 261–268

Citation in format AMSBIB
\Bibitem{BelMak17}
\by I.~N.~Belousov, A.~A.~Makhnev
\paper Automorphism groups of small distance-regular graphs
\jour Algebra Logika
\yr 2017
\vol 56
\issue 4
\pages 395--405
\mathnet{http://mi.mathnet.ru/al804}
\crossref{https://doi.org/10.17377/alglog.2017.56.401}
\transl
\jour Algebra and Logic
\yr 2017
\vol 56
\issue 4
\pages 261--268
\crossref{https://doi.org/10.1007/s10469-017-9447-4}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85033381061}


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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. V. V. Bitkina, A. A. Makhnev, “Automorphism group of a distanceregular graph with intersection array $\{35,32,1;1,4,35\}$”, Algebra and Logic, 56:6 (2018), 443–450  mathnet  crossref  crossref  isi
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