AI 中文总结
该研究基于群、拟群和环构造出4类阶为$2n^2$和$3n^2$的有向强正则图，推广了两类初步构造，得到指定参数的有向强正则图
AI 中文摘要
我们引入了4类阶为$2n^2$和$3n^2$的有向强正则图，其构造基于群、拟群、环及其拉丁方。两种初步的 wreath 积上的 Cayley 有向图构造被推广到任意拟群和环，得到参数分别为$(2n^2,3n-2,2n-1,n-1,3)$、$(2n^2,4n-2,2n+2,n+2,6)$、$(3n^2,4n-2,2n,n,4)$、$(3n^2,6n-2,2n+6,n+6,10)$的有向强正则图
英文摘要
We introduce four infinite families of directed strongly regular graphs of orders $2n^2$ and $3n^2$. The constructions are described in terms of groups, quasigroups, loops and their Latin squares. Two preliminary Cayley digraph constructions over wreath products are extended to arbitrary quasigroups and loops, yielding directed strongly regular graphs with parameters $(2n^2,3n-2,2n-1,n-1,3),(2n^2,4n-2,2n+2,n+2,6),(3n^2,4n-2,2n,n,4),(3n^2,6n-2,2n+6,n+6,10)$.
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