由次数 $n\leq 110$ 的传递群构造的拟强正则有向图
Quasi-strongly regular digraphs constructed from transitive groups of degree $n\leq 110$
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中文总结 AI 辅助
本文提出一种从传递置换群构造有向正则图的推广方法，证明多组参数的有向强正则图存在，并分类了低次数传递群和本原群产生的拟强正则有向图。
中文摘要 AI 辅助
本文提出了一种从传递置换群构造有向正则图的方法。该方法是文献\cite{dean1}中描述的从有限群构造传递1-设计的构造方法的推广。利用此构造，我们证明了参数为 $(72,25,15,6,10)$、$(96,11,4,3,1)$、$(96,22,16,8,4)$、$(96,26,11,7,7)$、$(96,29,23,10,8)$、$(96,42,32,16,20)$、$(96,45,35,22,20)$ 和 $(165,60,36,23,21)$ 的有向强正则图的存在性。最后，我们对次数至多 $30$ 的传递置换群以及次数从 $31$ 到 $110$ 且秩至多 $30$ 的本原置换群所产生的拟强正则有向图进行了分类。
英文摘要
In this paper we present a method for constructing directed regular graphs from a transitive permutation group. This method is a generalization of a construction method for transitive 1-designs from a finite group, described in \cite{dean1}. Using this construction, we prove the existence of directed strongly regular graphs with parameters $(72,25,15,6,10)$, $(96,11,4,3,1)$, $(96,22,16,8,4)$, $(96,26,11,7,7)$, $(96,29,23,10,8)$, $(96,42,32,16,20)$, $(96,45,35,22,20)$ and $(165,60,36,23,21)$. Finally, we classify quasi-strongly regular digraphs arising from transitive permutation groups of degree at most $30$ and from primitive permutation groups of degrees from $31$ to $110$ and rank at most $30$.
