论文标题
有限图的最佳嵌入和光谱间隙
Optimal embedding and spectral gap of a finite graph
论文作者
论文摘要
我们引入了一个关于图形嵌入欧几里得空间中的新优化问题，并讨论了它与Goering-Helmberg-Wappler引入的两个相互双重的优化问题的关系。我们证明，Goering等人的Laplace特征值最大化问题对于我们的嵌入优化问题也是双重的。我们解决了普通多边形和图形同构的优化问题，该问题是常规和半规则多面体的一骨。
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.
