论文标题
半等级环形图的顶点传递覆盖物
Vertex-transitive covers of semi-equivelar toroidal maps
论文作者
论文摘要
如果$ x $的自动形态组在$ x $的一组顶点上进行透支。如果地图中的所有顶点的面循环都是相同的类型，则该地图称为半等级。通常，表面上的半等级地图比顶点传递图更大。有半等级的环形图不是顶点传递的。在本文中，我们表明，半等级的环形图是顶点传播环形图的商。更明确地，我们证明每个半等级环形图具有有限的顶点传递盖。在2019年，drach {\ em等人}表明，每个顶点传播的环形图几乎具有最小的规则盖。因此，半等级的环形图是几乎规则的环形图的商。
A map $X$ on a surface is called vertex-transitive if the automorphism group of $X$ acts transitively on the set of vertices of $X$. If the face-cycles at all the vertices in a map are of same type then the map is called semi-equivelar. In general, semi-equivelar maps on a surface form a bigger class than vertex-transitive maps. There are semi-equivelar toroidal maps which are not vertex-transitive. In this article, we show that semi-equivelar toroidal maps are quotients of vertex-transitive toroidal maps. More explicitly, we prove that each semi-equivelar toroidal map has a finite vertex-transitive cover. In 2019, Drach {\em et al.} have shown that each vertex-transitive toroidal map has a minimal almost regular cover. Therefore, semi-equivelar toroidal maps are quotients of almost regular toroidal maps.
