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Trudy Inst. Mat. i Mekh. UrO RAN, 2017, Volume 23, Number 4, Pages 128–135 (Mi timm1473)  

Automorphisms of a distance-regular graph with intersection array $\{75,64,18,1;1,6,64,75\}$

A. Kh. Zhurtov, M. Kh. Shermetova

Kabardino-Balkarian State University named after H. M. Berbekov, Nalchik, 360004 Russia

Abstract: A distance-regular graph $\Gamma$ with intersection array $\{115,96,30,1;1,10,96,175\}$ is an $AT4$-graph. The antipodal quotient $\Gamma'$ has parameters $(392,115,18,40)$, and its first and second neighborhoods of vertices are strongly regular with parameters $(115,18,1,3)$ and $(276,75,10,24)$. Moreover, the second neighborhood of any vertex in $\Gamma_2(u)$ has intersection array $\{75,64,18,1;1,6,64,75\}$ and is a $4$-cover of a strongly regular graph with parameters $(276,75,10,24)$. Earlier, Makhnev, Paduchikh, and Samoilenko found possible automorphisms of a graph with parameters $(392,115,18,40)$ and of a graph with intersection array $\{115,96,30,1;1,10,96,175\}$. In this paper we find automorphisms of a graph with intersection array $\{75,64,18,1;1,6,64,75\}$. It is proved that the automorphism group of this graph acts intransitively on the set of its antipodal classes.

Keywords: distance-regular graph, automorphism of a graph.

Funding Agency Grant Number
Russian Science Foundation 14-11-00061-


DOI: https://doi.org/10.21538/0134-4889-2017-23-4-128-135

Full text: PDF file (194 kB)
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Bibliographic databases:

Document Type: Article
UDC: 519.17+512.54
MSC: 05B25
Received: 07.04.2017

Citation: A. Kh. Zhurtov, M. Kh. Shermetova, “Automorphisms of a distance-regular graph with intersection array $\{75,64,18,1;1,6,64,75\}$”, Trudy Inst. Mat. i Mekh. UrO RAN, 23, no. 4, 2017, 128–135

Citation in format AMSBIB
\Bibitem{ZhuShe17}
\by A.~Kh.~Zhurtov, M.~Kh.~Shermetova
\paper Automorphisms of a distance-regular graph with intersection array $\{75,64,18,1;1,6,64,75\}$
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2017
\vol 23
\issue 4
\pages 128--135
\mathnet{http://mi.mathnet.ru/timm1473}
\crossref{https://doi.org/10.21538/0134-4889-2017-23-4-128-135}
\elib{http://elibrary.ru/item.asp?id=30713967}


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