Tree Decomposition By Eigenvectors

Details Tree Decomposition By Eigenvectors Tree Decomposition By Eigenvectors

2011-12-14

arxiv.org/abs/1112.3193v1

Linear Algebra Appl., Vol. 430 (2009), pp. 133-144

Mathematics

Combinatorics

25 pages

Scientific paper

10.1016/j.laa.2008.07.015

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.

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