论文标题
连接到完整图的链条光谱
Spectra of chains connected to complete graphs
论文作者
论文摘要
我们表征了由连接到完整图的一个或两个有限或无限链组成的图形的laplacian的光谱。我们显示了两种类型的局部特征向量的存在，即完全消失在完整图外的特征向量和特征向量，它们在完整的图表外呈指数减小。我们的结果还意味着与局部和扩展特征向量相对应的特征值之间的差距。
We characterize the spectrum of the Laplacian of graphs composed of one or two finite or infinite chains connected to a complete graph. We show the existence of localized eigenvectors of two types, eigenvectors that vanish exactly outside the complete graph and eigenvectors that decrease exponentially outside the complete graph. Our results also imply gaps between the eigenvalues corresponding to localized and extended eigenvectors.
