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Diskr. Mat., 2009, Volume 21, Issue 1, Pages 78–104 (Mi dm1040)  

This article is cited in 2 scientific papers (total in 2 papers)

On the automorphisms of the strongly regular graph with parameters $(85, 14, 3, 2)$

D. V. Paduchikh


Abstract: Let $\Gamma$ be the strongly regular graph with parameters $(85, 14, 3, 2)$, $g$ be an element of prime order $p$ of $\operatorname{Aut}(\Gamma)$ and $\Delta=\operatorname{Fix}(g)$. In this paper, it is proved that either $p=5$ or $p=17$ and $\Delta$ is the empty graph, or $p=7$ and $\Delta$ is a 1-clique, or $p=5$ and $\Delta$ is a 5-clique, or $p=3$ and $\Delta$ is a quadrangle or a $2\times5$ lattice, or $p=2$ and $\Delta$ is a union of $\varphi$ isolated vertices and $\psi$ isolated triangles, $\psi=1$ and $\varphi\in\{4,6\}$ or $\psi=0$ and $\varphi=5$. In addition, it is shown that the graph $\Gamma$ is not vertex transitive.

DOI: https://doi.org/10.4213/dm1040

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English version:
Discrete Mathematics and Applications, 2009, 19:1, 89–111

Bibliographic databases:

UDC: 519.14
Received: 29.01.2007

Citation: D. V. Paduchikh, “On the automorphisms of the strongly regular graph with parameters $(85, 14, 3, 2)$”, Diskr. Mat., 21:1 (2009), 78–104; Discrete Math. Appl., 19:1 (2009), 89–111

Citation in format AMSBIB
\Bibitem{Pad09}
\by D.~V.~Paduchikh
\paper On the automorphisms of the strongly regular graph with parameters $(85, 14, 3, 2)$
\jour Diskr. Mat.
\yr 2009
\vol 21
\issue 1
\pages 78--104
\mathnet{http://mi.mathnet.ru/dm1040}
\crossref{https://doi.org/10.4213/dm1040}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2531031}
\elib{https://elibrary.ru/item.asp?id=20730280}
\transl
\jour Discrete Math. Appl.
\yr 2009
\vol 19
\issue 1
\pages 89--111
\crossref{https://doi.org/10.1515/DMA.2009.007}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-63849091496}


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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. Behbahani M., Lam C., “Strongly Regular Graphs with Non-Trivial Automorphisms”, Discrete Math., 311:2-3 (2011), 132–144  crossref  mathscinet  zmath  isi  scopus
    2. M. M. Isakova, A. A. Makhnev, A. A. Tokbaeva, “On graphs in which neighborhoods of vertices are strongly regular with parameters (85,14,3,2) or (325,54,3,10)”, Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 68–74  mathnet  crossref  crossref  mathscinet  isi  elib
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