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

VL - 309

SP - 341

EP - 353

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 2

ER -