Geodesic
Automorphisms of a distance-regular graph with intersection array {196, 156, 1; 1, 39, 196}
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 3, pp. 226-232

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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
Mots-clés : automorphism. 
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     author = {A. A. Tokbaeva},
     title = {Automorphisms of a distance-regular graph with intersection array {196, 156, 1; 1, 39, 196}},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {226--232},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2018_24_3_a19/}
}
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A. A. Tokbaeva. Automorphisms of a distance-regular graph with intersection array {196, 156, 1; 1, 39, 196}. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 3, pp. 226-232. http://geodesic.mathdoc.fr/item/TIMM_2018_24_3_a19/