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

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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. 
@article{SEMR_2021_18_2_a39,
     author = {A. A. Makhnev and M. S. Nirova},
     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},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a39/}
}
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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/