Tree decomposition by eigenvectors
Copyright policy )Tree decomposition by eigenvectors
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
- Institut für Mathematik Germany
- Clausthal University of Technology Germany
Primary 05C05, Numerical Analysis, Algebra and Number Theory, Secondary 15A03, 05C05 (Primary) 15A03 (Secondary), Eigenvector, Basis, Null space, FOS: Mathematics, Matching, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Geometry and Topology, Combinatorics (math.CO), Tree
Primary 05C05, Numerical Analysis, Algebra and Number Theory, Secondary 15A03, 05C05 (Primary) 15A03 (Secondary), Eigenvector, Basis, Null space, FOS: Mathematics, Matching, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Geometry and Topology, Combinatorics (math.CO), Tree
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