Geodesic
On pseudogeometrical graphs for some partial geometries
Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 1, pp. 117-127 
A. A. Makhnev. On pseudogeometrical graphs for some partial geometries. Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 1, pp. 117-127. http://geodesic.mathdoc.fr/item/FPM_2002_8_1_a9/
@article{FPM_2002_8_1_a9,
     author = {A. A. Makhnev},
     title = {On pseudogeometrical graphs for some partial geometries},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {117--127},
     year = {2002},
     volume = {8},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2002_8_1_a9/}
}
TY  - JOUR
AU  - A. A. Makhnev
TI  - On pseudogeometrical graphs for some partial geometries
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2002
SP  - 117
EP  - 127
VL  - 8
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/FPM_2002_8_1_a9/
LA  - ru
ID  - FPM_2002_8_1_a9
ER  - 
%0 Journal Article
%A A. A. Makhnev
%T On pseudogeometrical graphs for some partial geometries
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2002
%P 117-127
%V 8
%N 1
%U http://geodesic.mathdoc.fr/item/FPM_2002_8_1_a9/
%G ru
%F FPM_2002_8_1_a9

Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that a pseudogeometrical graph $\Gamma$ for $\mathrm{GQ}(4,12)$, containing a $49$-coclique $\mathcal O$, is a point graph of generalized quadrangle. Furthermore, the subgraph $\Gamma-\mathcal O$ is strongly regular with parameters $(196,39,2,9)$. It is proved that a pseudogeometrical graph for partial geometry $\mathrm{pG}_2(5,32)$ is locally a $\mathrm{GQ}(4,8)$-graph.

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

[2] Makhnev A. A., “Pseudogeometric graphs connected with partial geometries $pG(4,R,1)$”, Mathem. Forschunginst. Oberwolfach. Tagungsbericht, 32/91, 11

[3] Makhnev A. A., “O silno regulyarnom grafe s parametrami (64,18,2,6)”, Diskret. mat., 7:3 (1995), 121–128 | MR | Zbl

[4] Wilbrink H. A., Brouwer A. E., “(57,14,1) strongly regular graph does not exist”, Proc. Kon. Nederl. Akad. Ser. A, 45:1 (1983), 117–121 | MR | Zbl

[5] Paine S., Thas J., Finite generalized quadrangles, Pitman, Boston, 1985

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

[7] Cameron P., Goethals J.-M., Seidel J. J., “Strongly regular graphs having strongly regular subconstituents”, J. Algebra, 55:2 (1978), 257–280 | DOI | MR | Zbl