论文标题
图形覆盖有两个新的特征值
Graph covers with two new eigenvalues
论文作者
论文摘要
Hao Huang去年用来解决灵敏度猜想的某个符号签名的邻接矩阵与HyperCube的独特的，无4周的不含2倍的盖子密切相关。我们开发了一个框架，在该框架中，这种连接是几乎没有特征值的组标记的邻接矩阵和覆盖图的组合矩阵之间的关系的自然示例。特别是，我们将两个元素值盖定义为一个覆盖图，其邻接光谱（作为一个多键）与图形覆盖的图所覆盖的图形完全不同。我们表明，图表的行走规律性意味着任何Abelian双重盖盖的规律性。我们还给出了频谱表征，当时强图的循环两元值盖是距离的。
A certain signed adjacency matrix of the hypercube, which Hao Huang used last year to resolve the sensitivity conjecture, is closely related to the unique, 4-cycle free, 2-fold cover of the hypercube. We develop a framework in which this connection is a natural first example of the relationship between group labeled adjacency matrices with few eigenvalues, and combinatorially interesting covering graphs. In particular, we define a two-eigenvalue cover to be a covering graph whose adjacency spectra differs (as a multiset) from that of the graph it covers by exactly two eigenvalues. We show that walk regularity of a graph implies walk regularity of any abelian two-eigenvalue cover. We also give a spectral characterization for when a cyclic two-eigenvalue cover of a strongly-regular graph is distance regular.
