Geodesic
Automorphisms of a distance-regular graph with intersection array 176, 135, 32, 1; 1, 16, 135, 176
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 2, pp. 173-184 Cet article a éte moissonné depuis la source Math-Net.Ru

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A distance-regular graph $\Gamma$ with intersection array $\{176,135,32,1;1,16,135,176\}$ is an $AT4$-graph. Its antipodal quotient $\bar\Gamma$ is a strongly regular graph with parameters $(672,176$, $40,48)$. In both graphs the neighborhoods of vertices are strongly regular with parameters $(176,40,12,8)$. We study the automorphisms of these graphs. In particular, the graph $\Gamma$ is not arc-transitive. If $G=\mathrm{Aut}\,(\Gamma)$ contains an element of order 11, acts transitively on the vertex set of $\Gamma$, and $S(G)$ fixes each antipodal class, then the full preimage of the group $(G/S(G))'$ is an extension of a group of order 3 by $M_{22}$ or $U_6(2)$. We describe automorphism groups of strongly regular graphs with parameters $(176,40,12,8)$ and $(672,176,40,48)$ in the vertex-symmetric case.
Keywords: strongly regular graph, distance-regular graph
Mots-clés : graph automorphism. 
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A. A. Makhnev; D. V. Paduchikh. Automorphisms of a distance-regular graph with intersection array 176, 135, 32, 1; 1, 16, 135, 176. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 2, pp. 173-184. http://geodesic.mathdoc.fr/item/TIMM_2018_24_2_a15/

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