A. Makhnev and M. Samoilenko found intersection arrays of antipodal distance-regular graphs of diameter 3 and degree at most 1000 in which $\lambda=\mu$ and the neighborhoods of vertices are strongly regular. Automorphisms of distance-regular graphs in which the neighborhoods of vertices are strongly regular with second eigenvalue 3 except for graphs with intersection arrays $\{196,156,1;1,39,196\}$ and $\{205,136,1;1,68,205\}$ were found earlier. We find possible prime orders of elements in the automorphism group of a distance-regular graph with intersection array $\{196,156,1;1,39,196\}$ as well as their fixed-point subgraphs. It is proved that the automorphism group of this graph acts intransitively on the vertex set.
Keywords: distance-regular graph, automorphism
The paper was received by the Editorial Office on May 21, 2018.
Al’bina Aniuarovna Tokbaeva, Cand. Sci. (Phys.-Math.), Kabardino-Balkarian State University named after H.M.Berbekov, Nal’chik, 360004 Russia, e-mail: tok2506@mail.ru
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