Geodesic
On graphs the neighbourhoods of whose verticesare pseudo-geometric graphs for $GQ(3,3)$
Trudy Instituta matematiki, Tome 18 (2010) no. 1, pp. 28-35 
A. K. Gutnova; A. A. Makhnev. On graphs the neighbourhoods of whose verticesare pseudo-geometric graphs for $GQ(3,3)$. Trudy Instituta matematiki, Tome 18 (2010) no. 1, pp. 28-35. http://geodesic.mathdoc.fr/item/TIMB_2010_18_1_a3/
@article{TIMB_2010_18_1_a3,
     author = {A. K. Gutnova and A. A. Makhnev},
     title = {On graphs the neighbourhoods of whose verticesare pseudo-geometric graphs for $GQ(3,3)$},
     journal = {Trudy Instituta matematiki},
     pages = {28--35},
     year = {2010},
     volume = {18},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2010_18_1_a3/}
}
TY  - JOUR
AU  - A. K. Gutnova
AU  - A. A. Makhnev
TI  - On graphs the neighbourhoods of whose verticesare pseudo-geometric graphs for $GQ(3,3)$
JO  - Trudy Instituta matematiki
PY  - 2010
SP  - 28
EP  - 35
VL  - 18
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TIMB_2010_18_1_a3/
LA  - ru
ID  - TIMB_2010_18_1_a3
ER  - 
%0 Journal Article
%A A. K. Gutnova
%A A. A. Makhnev
%T On graphs the neighbourhoods of whose verticesare pseudo-geometric graphs for $GQ(3,3)$
%J Trudy Instituta matematiki
%D 2010
%P 28-35
%V 18
%N 1
%U http://geodesic.mathdoc.fr/item/TIMB_2010_18_1_a3/
%G ru
%F TIMB_2010_18_1_a3

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

Let $\mathcal{F}$ be a class of graphs. We call a graph $\Gamma$ a locally $\mathcal{F}$-graph if $[a]\in\mathcal{F}$ for every vertex $a$ of $\Gamma.$ Earlier for the class $\mathcal{F}$ consisting of pseudogeometrical graphs for $pG_{s-2}(s,t)$ the study of locally $\mathcal{F}$-graphs was reduced to investigating locally pseudo $GQ(3,t)$-graphs, $t\in\{3,5\}$. A description of completely regular locally pseudo $GQ(3,3)$-graphs is obtained in the paper.

[1] Gutnova A.K., Makhnev A.A., “O grafakh, v kotorykh okrestnosti vershin yavlyayutsya psevdogeometricheskimi grafami dlya $pG_{s-2}(s,t)$”, Doklady AN, 431:3 (2010), 301–305

[2] Haemers W., Spence E., “The pseudo-geometric graphs for generalized quadrangles of order $(3,t)$”, Eur. J. Comb., 22:6 (2001), 839–845 | DOI | MR | Zbl

[3] Makhnev A.A., “O rasshireniyakh chastichnykh geometrii, soderzhaschikh malye $\mu$-podgrafy”, Diskr. analiz i issled. operatsii, 3:3 (1996), 71–83 | MR | Zbl

[4] Brouwer A.E., Haemers W.H., Spectra of graphs (course notes), http://www.win.tue.nl/aeb

[5] Brouwer A.E., Cohen A.M., Neumaier A., Distance-Regular Graphs, Springer-Verlag, Berlin etc., 1989 | MR