Geodesic
Distance-regular graphs with intersection array $\{69,56,10;1,14,60\}$, $\{74,54,15;1,9,60\}$ and $\{119,100,15;1,20,105\}$ do not exist
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1254-1259 Cet article a éte moissonné depuis la source Math-Net.Ru

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Distance regular graphs $\Gamma$ of diameter 3 for which the graphs $\Gamma_2$ and $\Gamma_3$ are strongly regular, studied by M.S. Nirova. For $Q$-polynomial graphs with intersection arrays $\{69,56,10; 1,14,60\}$ and $\{119,100,15; 1, 20,105\}$ the graph $\Gamma_3$ is strongly regular and does not contain triangles. Automorphisms of graphs with these intersection arrays were found by A.A. Makhnev, M.S. Nirova and M.M. Isakova, A.A. Makhnev, respectively. The graph $\Gamma$ with the intersection array $\{74,54,15; 1,9,60\} $ also is $Q $-polynomial, and $\Gamma_3$ is a strongly regular graph with parameters $(630,111,12,21)$. It is proved in the paper that graphs with intersection arrays $\{69,56,10;1,14,60\}$, $\{74,54,15; 1,9,60\}$ and $\{119,100,15; 1,20, 105\} $ do not exist.
Keywords: distance-regular graph, triple intersection numbers. 
@article{SEMR_2019_16_a70,
     author = {A. A. Makhnev and M. M. Isakova and M. S. Nirova},
     title = {Distance-regular graphs with intersection array $\{69,56,10;1,14,60\}$, $\{74,54,15;1,9,60\}$ and $\{119,100,15;1,20,105\}$ do not exist},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1254--1259},
     year = {2019},
     volume = {16},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a70/}
}
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A. A. Makhnev; M. M. Isakova; M. S. Nirova. Distance-regular graphs with intersection array $\{69,56,10;1,14,60\}$, $\{74,54,15;1,9,60\}$ and $\{119,100,15;1,20,105\}$ do not exist. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1254-1259. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a70/

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