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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2017, Volume 23, Number 4, Pages 119–127
DOI: https://doi.org/10.21538/0134-4889-2017-23-4-119-127 (Mi timm1472) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Automorphisms of an $AT4(4,4,2)$-graph and of the corresponding strongly regular graphs

K. S. Efimovabc

a Ural Federal University, Ekaterinburg, 620002 Russia
b Ural State University of Economics, Ekaterinburg, 620144 Russia
c Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620990 Russia
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DOI: https://doi.org/10.21538/0134-4889-2017-23-4-119-127
Abstract: A.A. Makhnev, D.V. Paduchikh, and M. M. Khamgokova gave a classification of distance-regular locally\linebreak $GQ(5,3)$-graphs. In particular, there arises an $AT4(4,4,2)$-graph with intersection array $\{96,75,16,1;1,16,75,96\}$ on $644$ vertices. The same authors proved that an $AT4(4,4,2)$-graph is not a locally $GQ(5,3)$-graph. However, the existence of an $AT4(4,4,2)$-graph that is a locally pseudo $GQ(5,3)$-graph is unknown. The antipodal quotient of an $AT4(4,4,2)$-graph is a strongly regular graph with parameters $(322,96,20,32)$. These two graphs are locally pseudo $GQ(5,3)$-graphs. We find their possible automorphisms. It turns out that the automorphism group of a distance-regular graph with intersection array $\{96,75,16,1;1,16,75,96\}$ acts intransitively on the set of its antipodal classes.
Keywords: distance-regular graph, graph automorphism.
Funding agency Grant number
Russian Science Foundation 14-11-00061-П
Ministry of Education and Science of the Russian Federation 02.A03.21.0006
Received: 01.09.2017
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2019, Volume 304, Issue 1, Pages S59–S67
DOI: https://doi.org/10.1134/S008154381902007X
Bibliographic databases:
Document Type: Article
UDC: 519.17
MSC: 05B25
Language: Russian
Citation: K. S. Efimov, “Automorphisms of an $AT4(4,4,2)$-graph and of the corresponding strongly regular graphs”, Trudy Inst. Mat. i Mekh. UrO RAN, 23, no. 4, 2017, 119–127; Proc. Steklov Inst. Math. (Suppl.), 304, suppl. 1 (2019), S59–S67
Citation in format AMSBIB
\Bibitem{Efi17}
\by K.~S.~Efimov
\paper Automorphisms of an $AT4(4,4,2)$-graph and of the corresponding strongly regular graphs
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2017
\vol 23
\issue 4
\pages 119--127
\mathnet{http://mi.mathnet.ru/timm1472}
\crossref{https://doi.org/10.21538/0134-4889-2017-23-4-119-127}
\elib{https://elibrary.ru/item.asp?id=30713965}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2019
\vol 304
\issue , suppl. 1
\pages S59--S67
\crossref{https://doi.org/10.1134/S008154381902007X}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000453521700011}
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