与完全图连通的链的谱
Spectra of chains connected to complete graphs
摘要：
我们刻画了由一个或两个连接到完全图的有限或无限链组成的图的Laplacian的谱。我们证明了两种类型的局部特征向量的存在性，即完全消失在完全图之外的特征向量和指数下降在完全图之外的特征向量。我们的研究结果还意味着本地化和扩展的本征向量对应的本征值之间的差距。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
