Designs over edge-regular, co-edge-regular and amply regular graphs are investigated. Using linear algebra, we obtain lower bounds in certain inequalities involving the parameters of the designs. Some results on designs meeting the bounds are obtained. These designs are over connected regular graphs with least eigenvalue \(-2\), have the minimal number of blocks and do not appear in an earlier work. Partial classification such designs over strongly regular graphs with least eigenvalue \(-2\) is given.

中文翻译：

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设计特征值最小的正则图$$-2 $$-2

研究了边规则图，共边规则图和充分规则图的设计。使用线性代数，我们在涉及设计参数的某些不等式中获得了下界。获得了满足边界的设计的一些结果。这些设计是特征值\（-2 \）最小的连通正则图，具有最少的块数，因此不会出现在较早的工作中。在具有最小特征值\（-2 \）的强正则图上进行了部分分类，例如这种设计。