论文标题
在分开球和标准化的拉普拉斯特征值的加权光谱半径上
On weighted spectral radius of unraveled balls and normalized Laplacian eigenvalues
论文作者
论文摘要
对于图$ g $，以顶点$ v $为中心的半径$ r $的拆开球是$ g $的通用封面中的$ v $的Ball of Radius $ r $。我们在图形上的固定半径的无固定半径的加权光谱半径上获得了一个，边缘上有正权重，该光谱在边缘上有正权重，用于在$ s $ th（其中$ s \ ge 2 $）上呈现上限，最小的laplacian laplacian eigenvalue在次要假设下的不规则图的均值。此外，当$ s = 2 $时，结果可能被视为绑定到一类不规则图的Alon--Boppana类型。
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.
