TY - JOUR
T1 - One-point extensions of generalized hexagons and octagons
AU - Cuypers, H.
AU - De Wispelaere, A.
AU - Maldeghem, van, H.
PY - 2009
Y1 - 2009
N2 - In this note, we prove the uniqueness of the one-point extension of a generalized hexagon of order 2 and prove the non-existence of such an extension of any other finite generalized hexagon of classical order, different from the one of order 2, and of the known finite generalized octagons provided the following property holds: for any three points x, y and z of , the graph-theoretic distance from y to z in the derived generalized hexagon is the same as the distance from x to z in .
AB - In this note, we prove the uniqueness of the one-point extension of a generalized hexagon of order 2 and prove the non-existence of such an extension of any other finite generalized hexagon of classical order, different from the one of order 2, and of the known finite generalized octagons provided the following property holds: for any three points x, y and z of , the graph-theoretic distance from y to z in the derived generalized hexagon is the same as the distance from x to z in .
U2 - 10.1016/j.disc.2007.12.015
DO - 10.1016/j.disc.2007.12.015
M3 - Article
SN - 0012-365X
VL - 309
SP - 341
EP - 353
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 2
ER -