论文标题
编号图产品的测量生长
Geodesic Growth of Numbered Graph Products
论文作者
论文摘要
在本文中，我们研究了编号图产品的大地测量生长。这些是对右角的Coxeter基团的概括，定义为有限循环基团的图形产品。我们首先定义了一个称为链接定型性的图形理论条件，以及链接规范编号图之间的自然等效性，并表明与链接规则编号图相关的编号图产品必须具有相同的地理生长序列。接下来，我们得出了一个与链接规则图相关的右角coxeter基团的大地生长的公式。最后，我们找到了一个方程系统，可用于求解与不包含三角形且具有恒定顶点编号的链接定型图相对应的编号图产物的地球生长。
In this paper, we study geodesic growth of numbered graph products; these are a generalization of right-angled Coxeter groups, defined as graph products of finite cyclic groups. We first define a graph-theoretic condition called link-regularity, as well as a natural equivalence amongst link-regular numbered graphs, and show that numbered graph products associated to link-regular numbered graphs must have the same geodesic growth series. Next, we derive a formula for the geodesic growth of right-angled Coxeter groups associated to link-regular graphs. Finally, we find a system of equations that can be used to solve for the geodesic growth of numbered graph products corresponding to link-regular numbered graphs that contain no triangles and have constant vertex numbering.
