论文标题
周长六的立方顶点传递图
Cubic vertex-transitive graphs of girth six
论文作者
论文摘要
在本文中，获得了有限的简单立方顶点传递图的完整分类，该图是$ 6 $的。事实证明，除了$ 20 $顶点的Desargues图外，每个这样的图形要么是六角形瓷砖的骨架，要么是封闭的双曲线表面的弧线传输三角形的截断的骨架，要么是$ 6 $ -6 $-6 $ nocular tage a arc dih dih dih dih dih dih dih dih dih dih dih dih dih dih dih dih dih dih dih dih dih dih dih dih dih dih dih dih dih。还讨论了大于$ 6 $的周长的立方顶点传递图。
In this paper, a complete classification of finite simple cubic vertex-transitive graphs of girth $6$ is obtained. It is proved that every such graph, with the exception of the Desargues graph on $20$ vertices, is either a skeleton of a hexagonal tiling of the torus, the skeleton of the truncation of an arc-transitive triangulation of a closed hyperbolic surface, or the truncation of a $6$-regular graph with respect to an arc-transitive dihedral scheme. Cubic vertex-transitive graphs of girth larger than $6$ are also discussed.
