# A.Kh. Zhurtov, M.Kh. Shermetova. Automorphisms of a distance-regular graph with intersection array {75,64,18,1;1,6,64,75}...P. 128-135

A distance-regular graph $\Gamma$ with intersection array $\{115,96,30,1;1,10,96,175\}$ is an $AT4$-graph. The antipodal quotient $\bar \Gamma$ 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.

The paper was received by the Editorial Office on April 7, 2017

Archil Khazeshovich Zhurtov, Dr. Phys.-Math. Sci., Kabardino-Balkarian State University named after H.M. Berbekov, Nal’chik, 360004 Russia, e-mail: zhurtov_a@mail.ru

Mariyana Khusenovna Shermetova, doctoral student, Kabardino-Balkarian State University named afterH.M. Berbekov, Nal’chik, 360004 Russia, e-mail: mariyana1992@mail.ru

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