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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2016, Volume 13, Pages 972–986
DOI: https://doi.org/10.17377/semi.2016.13.078 (Mi semr727) 		 
Mathematical logic, algebra and number theory

Automorphisms of distance-regular graph with intersection array $\{117,80,18,1;1,18,80,117\}$

A. A. Makhnevab, D. V. Paduchikha, M. M. Khamgokovac

a Krasovskii Institute of Mathematics and Mechanics, ul. S.Kovalevskoi, 16, 620990, Ekaterinburg, Russia
b Uralskii Federalnii Universitet, ul. Mira, 19, 620002, Ekaterinburg, Russia
c Kabardino-Balkarskii University, ul. Mira, 16, 360000, Nalchik, Russia
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DOI: https://doi.org/10.17377/semi.2016.13.078
Abstract: Distance-regular graph $\Gamma$ with intersection array $\{117, 80, 18, 1; 1, 18, 80, 117\}$ is an $AT4$-graph. Antipodal quotient $\bar \Gamma$ has parameters $(378, 117, 36, 36)$. Both graphs have strongly regular neighbourhoods with parameters $(117, 36, 15, 9)$. In the work automorphisms of the said graphs are found. In particular, there exist graphs of rank 3 with parameters $(117, 36, 15, 9)$ and $(378, 117, 36, 36)$, and graph with intersection array $\{117, 80, 18, 1; 1, 18, 80, 117\}$ is not arc-transitive.
Keywords: strongly regular graph, eigenvalue, automorphism of graph.
Funding agency Grant number
Russian Science Foundation 15-11-10025
Ministry of Education and Science of the Russian Federation 02.A03.21.0006
Received July 25, 2016, published November 8, 2016
Bibliographic databases:
Document Type: Article
UDC: 519.17
MSC: 20C25
Language: English
Citation: A. A. Makhnev, D. V. Paduchikh, M. M. Khamgokova, “Automorphisms of distance-regular graph with intersection array $\{117,80,18,1;1,18,80,117\}$”, Sib. Èlektron. Mat. Izv., 13 (2016), 972–986
Citation in format AMSBIB
\Bibitem{MakPadKha16}
\by A.~A.~Makhnev, D.~V.~Paduchikh, M.~M.~Khamgokova
\paper Automorphisms of distance-regular graph with intersection array $\{117,80,18,1;1,18,80,117\}$
\jour Sib. \`Elektron. Mat. Izv.
\yr 2016
\vol 13
\pages 972--986
\mathnet{http://mi.mathnet.ru/semr727}
\crossref{https://doi.org/10.17377/semi.2016.13.078}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3576016}
\zmath{https://zbmath.org/?q=an:1373.05085}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000407781100078}
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