论文标题
图形设计和大风二元性
Graphical Designs and Gale Duality
论文作者
论文摘要
图形设计是图形顶点的一个子集，因此设计上某些图形特征向量的加权平均值与其全局平均值一致。我们使用大风双重性来表明常规图中的正加权图形设计与该图的广义本本植物的脸部进行了培训。该连接可用于组织，计算和优化设计。我们通过计算或界定最小的设计，平均频率顺序以外的最后一个特征空间，这说明了该工具在三个Cayley图形的家族中的功能 - 鸡尾酒会图，周期和高管的图。
A graphical design is a subset of graph vertices such that the weighted averages of certain graph eigenvectors over the design agree with their global averages. We use Gale duality to show that positively weighted graphical designs in regular graphs are in bijection with the faces of a generalized eigenpolytope of the graph. This connection can be used to organize, compute and optimize designs. We illustrate the power of this tool on three families of Cayley graphs -- cocktail party graphs, cycles, and graphs of hypercubes -- by computing or bounding the smallest designs that average all but the last eigenspace in frequency order.
