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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2019, Volume 16, Pages 1245–1253
DOI: https://doi.org/10.33048/semi.2019.16.086
(Mi semr1126)
 

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

Discrete mathematics and mathematical cybernetics

Automorphisms of small graphs with intersection array $\{nm-1, nm-n+m-1,n-m+1;1,1,nm-n+m-1\}$

M. P. Golubyatnikov

Krasovskii Institute of Mathematics and Mechanics, 16, S.Kovalevskaya str. Yekaterinburg, 620990, Russia.
Full-text PDF (157 kB) Citations (1)
References:
Abstract: Let $\Gamma$ be a distance regular graph of diameter 3 for which the graph $\Gamma_3$ is a pseudo-network.
Previously, A.A. Makhnev, M.P. Golubyatnikov, Wenbin Guo found infinite series of admissible arrays of intersections of such graphs. In the case of $c_2 = 1$, we have the two-parameter series $\{nm-1,nm-n+m-1,n-m+1;1,1,nm-n+m-1\}$.
Possible automorphisms of such graphs were found by A.A. Makhnev, M.P. Golubyatnikov.
In this paper the author found automorphism groups of distance regular graphs with intersection arrays $\{90,84,7;1,1,84\}$ ($n=13,m=7$), $\{220,216,5;1,1,216\}$ ($n=17,m=13$), $\{272,264,9;1,1,264\}$ ($n=21,m=13$). In particular, this graphs are not arc transitive.
Keywords: distance-regular graph, automorphism.
Funding agency Grant number
Russian Science Foundation 19-71-10067
Received August 27, 2019, published September 17, 2019
Bibliographic databases:
Document Type: Article
UDC: 519.17+512.54
MSC: 05C25
Language: Russian
Citation: M. P. Golubyatnikov, “Automorphisms of small graphs with intersection array $\{nm-1, nm-n+m-1,n-m+1;1,1,nm-n+m-1\}$”, Sib. Èlektron. Mat. Izv., 16 (2019), 1245–1253
Citation in format AMSBIB
\Bibitem{Gol19}
\by M.~P.~Golubyatnikov
\paper Automorphisms of small graphs with intersection array $\{nm-1, nm-n+m-1,n-m+1;1,1,nm-n+m-1\}$
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 1245--1253
\mathnet{http://mi.mathnet.ru/semr1126}
\crossref{https://doi.org/10.33048/semi.2019.16.086}
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  • https://www.mathnet.ru/eng/semr/v16/p1245
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Full-text PDF :133
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