Spectra of chains connected to complete graphs
Spectral Theory
2020-02-21 v1 Combinatorics
Abstract
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.
Cite
@article{arxiv.2002.08890,
title = {Spectra of chains connected to complete graphs},
author = {J. -G. Caputo and G. Cruz-Pacheco and A. Knippel and P. Panayotaros},
journal= {arXiv preprint arXiv:2002.08890},
year = {2020}
}