用超椭圆构造强正则图

在本中，我们证明了下面主要结果：如果U=（X，B）是一个t-(υ t,κ t,1）设计（t≥1),Y=(υ1，υ2，…，υt)∈X，用UY表示U在Y上的限制，如果D=UY是一个2-对称设计，并且D中的超椭圆的个数至多为tυ(υ-1)(υ-κ)/κ(κ^2-1)]，则这些超椭圆可以分为t类，每一类构成一个2-设计，它们的块图都是强正则图，并且它们的并也是一个2-设计，作为一个推论，我们给出了一个2-设计可以扩张的判据，最后我们给出一个例子说明我们的方法有效。

Constructing new strongly regular graphs with hyperovals

In this paper, we have proved the following main results.. If UY=(X, B) is a (t+2)-(v+t, k+t, 1) design (t≥1), Y={v1, v2, …vt}X. By UY we denote the restriction of U on Y. If D=UY is a square 2-(v, k, 1) design and the number of hyperovals in D is at most tv(v-1)(v-k)/k(k2-1),then these hyperovals can be divided into t classes, each of them contributes a 2-design and block graphs of them are strongly regular. Furthermore, the union of these designs is also a 2-design. As a corollary, we give a criterion of which design is extendable. Finally, we give an example illustrating that our method works effectively.