Tree Decomposition By Eigenvectors
arXiv:1112.3193 · doi:10.1016/j.laa.2008.07.015
Abstract
In this work a composition-decomposition technique is presented that correlates tree eigenvectors with certain eigenvectors of an associated so-called skeleton forest. In particular, the matching properties of a skeleton determine the multiplicity of the corresponding tree eigenvalue. As an application a characterization of trees that admit eigenspace bases with entries only from the set {0, 1,-1} is presented. Moreover, a result due to Nylen concerned with partitioning eigenvectors of tree pattern matrices is generalized.
25 pages