论文标题
对平面中的全球刚性边缘传输图和距离规则图进行分类
Classifying the globally rigid edge-transitive graphs and distance-regular graphs in the plane
论文作者
论文摘要
如果该图在欧几里得平面中的几乎所有嵌入将定义一个具有唯一（静电）解决方案的边缘长度方程系统，则据说图形是全球刚性的。在2007年，杰克逊（Jackson），Servatius和Servatius确切地表征了哪些顶点传播图仅通过其程度和最大集团数字上的全球刚度，这两个易于计算的顶点传播图。在此简短的说明中，我们将将此特征扩展到由其自动形态组确定的所有图。我们通过准确表征哪些边缘传输图和距离规则图的最小程度和最大程度在全局刚性上进行做到这一点。
A graph is said to be globally rigid if almost all embeddings of the graph's vertices in the Euclidean plane will define a system of edge-length equations with a unique (up to isometry) solution. In 2007, Jackson, Servatius and Servatius characterised exactly which vertex-transitive graphs are globally rigid solely by their degree and maximal clique number, two easily computable parameters for vertex-transitive graphs. In this short note we will extend this characterisation to all graphs that are determined by their automorphism group. We do this by characterising exactly which edge-transitive graphs and distance-regular graphs are globally rigid by their minimal and maximal degrees.
