Geodesic
On automorphisms of distance-regular graphs with intersection arrays $\{2r+1,2r-2,1;1,2,2r+1\}$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 2, pp. 28-37 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\Gamma$ be an antipodal graph with intersection array $\{2r+1,2r-2,1;1,2,2r+1\}$, where $2r(r+1)\le 4096$. If $2r+1$ is a prime power, then Mathon's scheme provides the existence of an edge-symmetric graph with this intersection array. Note that $2r+1$ is not a prime power only for $r\in \{7,17,19,22,25,27,31,32,37,38,42,43\}$. We study automorphisms of hypothetical distance-regular graphs with the specified values of $r$. The cases $r\in \{7,17,19\}$ were considered earlier. We prove that, if $\Gamma$ is a vertex-symmetric graph with intersection array $\{2r+1,2r-2,1;1,2,2r+1\}$, $2r+1$ is not a prime power, and $r\le 43$, then $r=25,27,31$.
Keywords: distance-regular graph
Mots-clés : graph automorphism. 
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I. N. Belousov; A. A. Makhnev. On automorphisms of distance-regular graphs with intersection arrays $\{2r+1,2r-2,1;1,2,2r+1\}$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 2, pp. 28-37. http://geodesic.mathdoc.fr/item/TIMM_2016_22_2_a3/

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