论文标题
特征分类，光谱多型和边缘传递性
Eigenpolytopes, Spectral Polytopes and Edge-Transitivity
论文作者
论文摘要
从有限的简单图$ g $开始，对于其邻接矩阵的每个特征值$θ$，一个人都可以构建一个convex polytope $ p_g（θ）$，所谓的$θ$ -EIGENPOLYTOP的$ G $。对于某些多面体，该技术可用于从其边缘图中重建多面体。这样的多面有（我们称它们为光谱）仍然很熟悉。我们概述了本征多型和光谱多型的文献。 我们引入了几何条件，通过该条件证明给定的多面体是光谱（更准确地说，$θ_2$ - 光谱）。我们将此标准应用于边缘传播的多面体。我们表明，每个边缘传输多层均为$θ_2$ - 谱，由此图独特地确定，并实现了其所有对称性。我们提供了距离传播多面体的完整分类。
Starting from a finite simple graph $G$, for each eigenvalue $θ$ of its adjacency matrix one can construct a convex polytope $P_G(θ)$, the so called $θ$-eigenpolytop of $G$. For some polytopes this technique can be used to reconstruct the polytopes from its edge-graph. Such polytopes (we shall call them spectral) are still badly understood. We give an overview of the literature for eigenpolytopes and spectral polytopes. We introduce a geometric condition by which to prove that a given polytope is spectral (more exactly, $θ_2$-spectral). We apply this criterion to the edge-transitive polytopes. We show that every edge-transitive polytope is $θ_2$-spectral, is uniquely determined by this graph, and realizes all its symmetries. We give a complete classification of distance-transitive polytopes.
