发表机构
Alvernia University; University of Wyoming（阿尔弗尼亚大学; 怀俄明大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为强正则图双覆盖生成的4类结合方案给出必要条件，并据此证明了四类特定参数的距离正则图不存在，同时推广到一般交集数组情形。
AI 中文摘要
本文给出了由强正则图的双覆盖生成的4类结合方案的必要条件。这些条件被应用于直径4的对径距离正则图的开放情形。利用这些条件，我们证明了Brouwer、Cohen和Neumeier表中的四种情形不存在：{20,18,3,1;1,3,18,20}、{22,21,3,1;1,3,21,22}、{54,50,5,1;1,5,50,54}、{170,162,9,1;1,9,162,170}。更一般地，我们证明不存在具有交集数组{k,b1,b2,1;1,b2,b1,k}的距离正则图，其中b2≠1且(k b1/4)(1+k+k b1/(2b2))为奇数。文中还给出了由强正则图的双覆盖生成的更一般的4类结合方案的表格。
英文摘要
In this paper we give necessary conditions for 4-class association schemes that are generated by double covers of strongly regular graphs. These conditions are applied to open cases for diameter 4 antipodal distance-regular graphs. Using these conditions we are able to show the nonexistence of four cases in the table of Brouwer, Cohen and Neumeier: $\{20,18,3,1;1,3,18,20\}$, $\{22,21,3,1;1,3,21,22\}$, $\{ 54,50,5,1;,1,5,50,54 \}$, $\{ 170,162,9,1;,1,9,162,170 \}$. More generally, we show there is no distance-regular graph with intersection array $\{k,b_1,b_2,1;1,b_2,b_1,k \}$ where $b_2 \neq 1$ and $\frac{ k b_1 }{4}(1+k+\frac{ k b_1 }{2b_2})$ is odd. Tables are also given for more general 4-class association schemes generated by double covers of strongly regular graphs.
