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
Cet article a éte moissonné depuis 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.
@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 -
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/
[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