有限图的最优嵌入与谱间隙
Optimal embedding and spectral gap of a finite graph
摘要：
我们引入了一个新的最优化问题关于嵌入到一个欧几里得空间的图，并讨论其关系的两个，相互对偶，由戈林-赫尔姆堡-瓦普勒介绍的最优化问题。我们证明了戈林等人的拉普拉斯特征值最大化问题也是我们的嵌入最优化问题的对偶问题。本文解决了广义多边形和同构于正、半正多面体的一元图的最优化问题。
英文摘要：
We introduce a new optimization problem regarding embeddings of a graph into a Euclidean space and discuss its relation to the two, mutually dual, optimizations problems introduced by Goering-Helmberg-Wappler. We prove that the Laplace eigenvalue maximization problem of Goering et al is also dual to our embedding optimization problem. We solve the optimization problems for generalized polygons and graphs isomorphic to the one-skeltons of regular and semi-regular polyhedra.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
