解球的加权谱半径与正规化拉普拉斯特征值
On weighted spectral radius of unraveled balls and normalized Laplacian eigenvalues
摘要：
对于图$G$，以顶点$v$为中心的半径为$r$的未展开球是$G$的泛覆盖中以$v$为中心的半径为$r$的球。本文给出了边权为正的图中固定半径的未拆球的加权谱半径的一个下界，并在较小的假设下给出了不规则图的$s$ -th（其中$s\ge 2$）最小归一化Laplacian特征值的一个上界.而且，当满足$s=2$时，对于一类不正则图，该结果可视为Alon-Boppana型界.
英文摘要：
For a graph $G$, the unraveled ball of radius $r$ centered at a vertex $v$ is the ball of radius $r$ centered at $v$ in the universal cover of $G$. We obtain a lower bound on the weighted spectral radius of unraveled balls of fixed radius in a graph with positive weights on edges, which is used to present an upper bound on the $s$-th (where $s\ge 2$) smallest normalized Laplacian eigenvalue of irregular graphs under minor assumptions. Moreover, when $s=2$, the result may be regarded as an Alon--Boppana type bound for a class of irregular graphs.
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