Tree Decomposition By Eigenvectors
Combinatorics
2018-08-21 v1
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.
Keywords
Cite
@article{arxiv.1112.3193,
title = {Tree Decomposition By Eigenvectors},
author = {Torsten Sander and Jürgen W. Sander},
journal= {arXiv preprint arXiv:1112.3193},
year = {2018}
}
Comments
25 pages