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Trudy Inst. Mat. i Mekh. UrO RAN, 2009, Volume 15, Number 2, Pages 162–176 (Mi timm232)  

This article is cited in 1 scientific paper (total in 2 paper)

On the automorphism group of the Aschbacher graph

A. A. Makhnev, D. V. Paduchikh

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

Abstract: A Moore graph is a regular graph of degree $k$ and diameter $d$ with $v$ vertices such that $v\le1+k+k(k-1)+…+k(k-1)^{d-1}$. It is known that a Moore graph of degree $k\ge3$ has diameter 2, i.e., it is strongly regular with parameters $\lambda=0$, $\mu=1$ and $v=k^2+1$, where the degree $k$ is equal to 3, 7, or 57. It is unknown whether there exists a Moore graph of degree $k=57$. Aschbacher showed that a Moore graph with $k=57$ is not a graph of rank 3. In this connection, we call a Moore graph with $k=57$ the Aschbacher graph and investigate its automorphism group $G$ without additional assumptions (earlier, it was assumed that $G$ contains an involution).

Keywords: automorphism group of a graph, Moore graph, strongly regular graph

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2009, 267, suppl. 1, S149–S163

Bibliographic databases:

UDC: 519.17+512.54
Received: 10.12.2008

Citation: A. A. Makhnev, D. V. Paduchikh, “On the automorphism group of the Aschbacher graph”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 2, 2009, 162–176; Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S149–S163

Citation in format AMSBIB
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\by A.~A.~Makhnev, D.~V.~Paduchikh
\paper On the automorphism group of the Aschbacher graph
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 2
\pages 162--176
\mathnet{http://mi.mathnet.ru/timm232}
\elib{http://elibrary.ru/item.asp?id=12878778}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2009
\vol 267
\issue , suppl. 1
\pages S149--S163
\crossref{https://doi.org/10.1134/S0081543809070141}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000274041900014}


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    This publication is cited in the following articles:
    1. V. A. Melentev, “Kompaktnye struktury vychislitelnykh sistem i ikh sintez”, UBS, 32 (2011), 241–261  mathnet
    2. “Makhnev Aleksandr Alekseevich (on his 60th birthday)”, Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), 1–11  mathnet  crossref  mathscinet
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