Geodesic
Distance-regular Terwilliger graphs with intersection arrays $\{50,42,1;1,2,50\}$ and $\{50,42,9;1,2,42\}$ do not exist
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1075-1082 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\Gamma$ be a distance-regular graph and its local subgraphs are isomorphic the Hoffman-Singleton graph. A.L. Gavrilyuk and A.A. Makhnev proved that $\Gamma$ is the Terwilliger graph with intersection array $\{50,42,9;1,2,42\}$ or $\{50,42,1;1,2,50\}$. In this paper we prove that Terwilliger graphs with intersection arrays $\{50,42,1;1,2,50\}$ and $\{50,42,9;1,2,42\}$ do not exist.
Keywords: distance-regular graph, Terwilliger graph, triple intersection numbers. 
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     title = {Distance-regular {Terwilliger} graphs with intersection arrays $\{50,42,1;1,2,50\}$ and $\{50,42,9;1,2,42\}$ do not exist},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1075--1082},
     year = {2021},
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A. A. Makhnev; M. S. Nirova. Distance-regular Terwilliger graphs with intersection arrays $\{50,42,1;1,2,50\}$ and $\{50,42,9;1,2,42\}$ do not exist. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1075-1082. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a39/

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[2] A.A. Makhnev, “Graphs in which neighborhoods of vertices are isomorphic to the Hoffman-Singleton graph”, Proc. Steklov Inst. Math., 267, Suppl. 1 (2009), S128–S148 | Zbl

[3] A.L. Gavrilyuk, A.A. Makhnev, “On distance-regular graphs in which the neighborhood of each vertex is isomorphic to the Hoffman-Singleton graph”, Dokl. Math., 80:2 (2009), 665–668 | DOI | Zbl

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