Classification of extended generalized quadrangles with maximum diameter

✍ Scribed by Alberto Del Fra; Dina Ghinelli

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 688 KB
• Volume: 105
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(92)90128-3

✦ Synopsis

Del Fra, A. and D. Ghinelli, Classification of extended generalized quadrangles with maximum diameter, Discrete Mathematics 105 (1992) 13-23. Let S be an extended generalized quadrangle of order (s, t). Recently it has been proved that the diameter A of the point-graph S satisfies A s s + 1 (see Cameron, Hughes and Pasini [4]

). In this paper we prove that A = s + 1 if and only if one of the following occurs:

(i) f = 1 and S is isomorphic to the Johnson geometry on ('~~,')) points (s > 0).

(ii) s = 2, t = 2,4 and S is isomorphic to the aftine polar space of order 2 and type A,, D;

on 32 and 56 points respectively. (iii) s = 1 and S is complete tripartite on 3(t + 1) points (t > 1).