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Journal of Siberian Federal University. Mathematics & Physics, 2017, Volume 10, Issue 3, Pages 271–280
DOI: https://doi.org/10.17516/1997-1397-2017-10-3-271-280 (Mi jsfu552) 		 
Automorphisms of the $AT4(6,6,3)$-graph and its strongly-regular graphs

Konstantin S. Efimovab, Aleksandr A. Makhnevcb

a Ural State University of Economics, 8 marta, 62, Yekaterinburg, 620144, Russia
b Ural Federal University, Mira, 19, Yekaterinburg, 620000, Russia
c N.N.Krasovsky Institute of Mathematics and Mechanics, S.Kovalevskoy, 4, Yekaterinburg, 620990, Russia
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DOI: https://doi.org/10.17516/1997-1397-2017-10-3-271-280
Abstract: Koolen and Jurisich defined class of $AT4$-graphs (tight antipodal graph of diameter $4$). Among these graphs available graph with intersection array $\{288,245,48,1;1,24,245,288\}$ on $v=1+288+2940+576+2=3807$ vertices. Antipodal quotient of this graph is strongly regular graph with parameters $(1269,288,42,72)$. Both these graphs are locally pseudo $GQ(7,5)$-graphs. In this paper we find possible automorphisms of these graphs. In particular, group of automorphisms of distance-regular graph with intersection array $\{288,245,48,1;1,24,245,288\}$ acts intransitive on the set of its antipodal classes.
Keywords: distance-regular graph, strongly-regular graph, automorphism of the graph.
Received: 02.11.2016
Received in revised form: 10.12.2016
Accepted: 20.02.2017
Bibliographic databases:
Document Type: Article
UDC: 519.17+512.54
Language: English
Citation: Konstantin S. Efimov, Aleksandr A. Makhnev, “Automorphisms of the $AT4(6,6,3)$-graph and its strongly-regular graphs”, J. Sib. Fed. Univ. Math. Phys., 10:3 (2017), 271–280
Citation in format AMSBIB
\Bibitem{EfiMak17}
\by Konstantin~S.~Efimov, Aleksandr~A.~Makhnev
\paper Automorphisms of the $AT4(6,6,3)$-graph and its strongly-regular graphs
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2017
\vol 10
\issue 3
\pages 271--280
\mathnet{http://mi.mathnet.ru/jsfu552}
\crossref{https://doi.org/10.17516/1997-1397-2017-10-3-271-280}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000412015000001}
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    		Журнал Сибирского федерального университета. Серия "Математика и физика"
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