| Abstract: | A set Δ of vertices of a generalized quadrangle of order (s, t) is said to be a hyperoval if any line intersects Δ in either 0, or 2 points. A hyperoval Δ is called an affine ovoid if
|Δ|=2st. It is well known that μ-subgraphs in triangular extensions of generalized quadrangles are hyperovals. In the present paper
we prove that ifS is a triangular extension forGQ(s, t) with totally regular point graph Γ such that μ=2st, thens is even, Γ is an τ-antipodal graph of diameter 3 with τ=1+s/2, and eithers=2, ort=s+2.
Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 266–271, August, 2000. |
