论文标题
在非阿布尔群体上有强烈常规的凯利图表上，带有Abelian子组的指数$ 2 $
On directed strongly regular Cayley graphs over non-abelian groups with an abelian subgroup of index $2$
论文作者
论文摘要
1988年，杜瓦尔（Duval）介绍了定向强的图形的概念，可以将其视为强烈规则图的有向图版本。这样的有向图具有与强规图相似的结构和代数特性。在过去的三十年中，发现Cayley图表，尤其是二面体群体的图形在构造有指导性的定期图中起着关键作用。在本文中，我们关注的是，在更多的一般群体上，有针对性的定期cayley图的表征。令$ g $为一个非阿布尔集团，带有Abelian索引$ 2 $。我们给出了一些必要的条件，以高于$ g $的cayley图，以强烈定期定期，并在满足指定条件的$ g $上定向了强烈的常规Cayley图。这扩展了He和Zhang（2019）的一些先前结果。
In 1988, Duval introduced the concept of directed strongly regular graphs, which can be viewed as a directed graph version of strongly regular graphs. Such directed graphs have similar structural and algebraic properties to strongly regular graphs. In the past three decades, it was found that Cayley graphs, especially those over dihedral groups, play a key role in the construction of directed strongly regular graphs. In this paper, we focus on the characterization of directed strongly regular Cayley graphs over more general groups. Let $G$ be a non-abelian group with an abelian subgroup of index $2$. We give some necessary conditions for a Cayley graph over $G$ to be directed strongly regular, and characterize the directed strongly regular Cayley graphs over $G$ satisfying specified conditions. This extends some previous results of He and Zhang (2019).
