Geodesic
Pseudo-geometric graphs of the partial geometries $pG_2(4,t)$
Diskretnaya Matematika, Tome 12 (2000) no. 1, pp. 113-134
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We prove that a strongly regular graph $\Gamma$ with parameters $$ (10t+5,4t+4,t+3,2t+2), $$ which contains a bad triple coincides with the graph $T(6)$ or with $\bar J(8,4)$. We say that a triple of vertices is bad if these vertices are not pairwise adjacent and the intersection of their neighbourhoods is empty. As a corollary, we establish the fact that any $\lambda$-subgraph of $\Gamma$ consists of isolated vertices and triangles. This research was supported by the Russian Foundation for Basic Research, grant 99–01–00462. 
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A. A. Makhnev. Pseudo-geometric graphs of the partial geometries $pG_2(4,t)$. Diskretnaya Matematika, Tome 12 (2000) no. 1, pp. 113-134. http://geodesic.mathdoc.fr/item/DM_2000_12_1_a9/

[1] Brauver A. E., Lint I. Kh., “Silno regulyarnye grafy i chastichnye geometrii”, Kibern. sbornik, 24 (1987), 186–229

[2] Goethals J. M., Seidel J. J., “The regular two graph on 276 points”, Discrete Math., 12:1 (1975), 143–158 | DOI | MR | Zbl

[3] Spence E., “Is Taylor's graph geometric?”, Discrete Math., 106–107 (1975), 143–158 | MR

[4] Makhnev A. A., “O psevdogeometricheskikh grafakh chastichnykh geometrii $pG_2(4,t)$”, Matem. sbornik, 187:7 (1996), 97–112 | MR | Zbl

[5] Wilbrink H. A., Brouwer A. E., “$(57,14,1)$ strongly regular graph does not exist”, Proc. Kon. Nederl. Akad., Ser. A., 45, no. 1, 1983, 117–121 | MR | Zbl

[6] Blokhuis A., Brouwer A. E., “Locally 4-by-4 grid graphs”, J. Graph Theory, 13:2 (1989), 229–244 | DOI | MR | Zbl