New Distance Regular Graphs Arising from Dimensional Dual Hyperovals

✍ Scribed by Antonio Pasini; Satoshi Yoshiara

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 156 KB
• Volume: 22
• Category: Article
• ISSN: 0195-6698
• DOI: 10.1006/eujc.2001.0501

✦ Synopsis

In we have studied the semibiplanes e m,h = A f (S e m,h ) obtained as affine expansions of the d-dimensional dual hyperovals of Yoshiara . We continue that investigation here, but from a graph theoretic point of view. Denoting by e m,h the incidence graph of (the point-block system of) e m,h , we prove that e m,h is distance regular if and only if either m + h = e or (m + h, e) = 1. In the latter case, e m,h has the same array as the coset graph K e h of the extended binary Kasami code K (2 e , 2 h ) but, as we prove in this paper, we have e m,h ∼ = K e h if and only if m = h. Finally, by exploiting some information obtained on e m,h , we prove that if e ≤ 13 and m = h with (m + h, e) = 1, then e m,h is simply connected.