论文标题
高度对称图的对称和光谱实现
Symmetric and Spectral Realizations of Highly Symmetric Graphs
论文作者
论文摘要
图形的实现$ g =（v，e）$是映射$ v \ colon v \ to \ bbb r^d $，它分配给每个顶点，$ d $ d $ d $ d $ - 二维欧几里得空间。我们从表示理论的角度（表达某些对称性），光谱图理论（满足某些自我压力条件）和刚性理论（承认不会改变对称属性的变形）的角度研究图形实现。 我们探讨了这些观点之间的联系，重点是实现高度对称图（ARC传输/距离传播）以及确保实现实现是平衡，频谱，刚性等需要多少对称性的问题。 我们包括许多示例，以广泛概述对称和光谱图实现的可能性和限制。
A realization of a graph $G=(V,E)$ is a map $v\colon V\to\Bbb R^d$ that assigns to each vertex a point in $d$-dimensional Euclidean space. We study graph realizations from the perspective of representation theory (expressing certain symmetries), spectral graph theory (satisfying certain self-stress conditions) and rigidity theory (admitting deformations that do not alter the symmetry properties). We explore the connections between these perspectives, with a focus on realizations of highly symmetric graphs (arc-transitive/distance-transitive) and the question of how much symmetry is necessary to ensure that a realization is balanced, spectral, rigid etc. We include many examples to give a broad overview of the possibilities and restrictions of symmetric and spectral graph realizations.
