Geodesic
Extensions of $\mathit{GQ}(4,2)$, the completely regular case
Diskretnaya Matematika, Tome 13 (2001) no. 3, pp. 91-109.

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

The description of extensions of generalised quadrangles $\mathit{GQ}(s,t)$ with flag-transitive group of automorphisms is known. For $s=3$, in a series of researches a description of extensions was given, with no assumptions on the action of the group of automorphisms. While investigating extensions of $\mathit{GQ}(4,2)$, the former author has given the structure of hyperovals of $\mathit{GQ}(4,2)$ and proved that there exist no totally regular locally $\mathit{GQ}(4,2)$ graphs with $\mu=10$. In the present paper, we conclude the classification of totally regular locally $\mathit{GQ}(4,2)$-graphs. This research was supported by the Russian Foundation for Basic Research, grant 99–01–00462. 
@article{DM_2001_13_3_a6,
     author = {A. A. Makhnev and D. V. Paduchikh},
     title = {Extensions of $\mathit{GQ}(4,2)$, the completely regular case},
     journal = {Diskretnaya Matematika},
     pages = {91--109},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2001_13_3_a6/}
}
TY  - JOUR
AU  - A. A. Makhnev
AU  - D. V. Paduchikh
TI  - Extensions of $\mathit{GQ}(4,2)$, the completely regular case
JO  - Diskretnaya Matematika
PY  - 2001
SP  - 91
EP  - 109
VL  - 13
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2001_13_3_a6/
LA  - ru
ID  - DM_2001_13_3_a6
ER  - 
%0 Journal Article
%A A. A. Makhnev
%A D. V. Paduchikh
%T Extensions of $\mathit{GQ}(4,2)$, the completely regular case
%J Diskretnaya Matematika
%D 2001
%P 91-109
%V 13
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2001_13_3_a6/
%G ru
%F DM_2001_13_3_a6
A. A. Makhnev; D. V. Paduchikh. Extensions of $\mathit{GQ}(4,2)$, the completely regular case. Diskretnaya Matematika, Tome 13 (2001) no. 3, pp. 91-109. http://geodesic.mathdoc.fr/item/DM_2001_13_3_a6/

[1] Buekenhout F., Hubaut X., “Locally polar spaces and related rank 3 groups”, J. Algebra, 45:2 (1997), 391–434 | DOI | MR

[2] Makhnev A. A., “O silno regulyarnykh rasshireniyakh obobschennykh chetyrekhugolnikov s korotkimi pryamymi”, Diskretnaya matematika, 8:3 (1996), 31–39 | MR | Zbl

[3] Makhnev A. A., “Rasshireniya $\mathit{GQ}(4,2)$, opisanie giperovalov”, Diskretnaya matematika, 9:3 (1997), 101–116 | MR | Zbl

[4] Makhnev A. A., “Some partial geometries with extremal parameters”, Abstr. Intern. Conf. Finite Geometry and Combinatorics (18-24 May), 1997, 79–80

[5] Pain S., Thas J. A., Finite generalized quadrangles, Pitman, Boston, 1984

[6] Brouwer A. E., Cohen A. M., Neumaier A., Distance-regular graphs, 1989, Springer, Berlin | MR | Zbl

[7] Godsil C. D., “Covers of complete graphs”, Advanced Studies in Pure Math., 24 (1996), 137–163 | MR | Zbl

[8] Brouwer A. E., Wilbrink H. A., “Ovoids and fans in the generalized quadrangle $Q(4,2)$”, Geom. Dedicata, 36:1 (1990), 121–124 | DOI | MR | Zbl