论文标题
立方顶点传递图承认大阶的自动形态
Cubic vertex-transitive graphs admitting automorphisms of large order
论文作者
论文摘要
订单$ n $的连接图，承认订单$ n/k $的半自动形态被称为$ k $ - 万月循环。已经对小价值的高度对称多循环剂进行了广泛的研究，并且对于立方顶点和电弧传输的多回路存在几个分类结果。在本文中，我们研究了订单$ n $的更广泛的立方顶点传递图，承认订单$ n/3 $或更大的订单的自动形态可能不是半毛病。特别是，我们表明，任何此类图都是一些$ K \ leq 3 $的$ K $ Multicriculant，或者属于Girth $ 6 $的无限图。
A connected graph of order $n$ admitting a semiregular automorphism of order $n/k$ is called a $k$-multicirculant. Highly symmetric multicirculants of small valency have been extensively studied, and several classification results exist for cubic vertex- and arc-transitive multicirculants. In this paper we study the broader class of cubic vertex-transitive graphs of order $n$ admitting an automorphism of order $n/3$ or larger that may not be semiregular. In particular, we show that any such graph is either a $k$-multicirculant for some $k \leq 3$, or it belongs to an infinite family of graphs of girth $6$.
