On the Null Space Structure Associated with Trees and Cycles

Authors

Shaun M. Fallat, University of Regina
Shahla Nasserasr, University of ReginaFollow

Document Type

Article

Publication Date

5-1-2013

Publication Title

Journal of Combinatorial Mathematics and Combinatorial Computing (JCMCC)

Keywords

Cycle, Eigenvector, Multiplicity, Null space, Schur complement, Independent vertices, Tree, Positive semidefinite matrix

ISSN

0835-3026

Volume

85

Issue/No.

Special volume for Kieka Mynhardt

First Page

253

Last Page

272

Abstract

In this work, we study the structure of the null spaces of matrices associated with graphs. Our primary tool is utilizing Schur complements based on certain collections of independent vertices. This idea is applied in the case of trees, and seems to represent a unifying theory within the context of the support of the null space. We extend this idea and apply it to describe the null vectors and corresponding nullities of certain symmetric matrices associated with cycles

Comments

2000 MSC: 05C50, 15A18

NSUWorks Citation

Fallat, Shaun M. and Nasserasr, Shahla, "On the Null Space Structure Associated with Trees and Cycles" (2013). Mathematics Faculty Articles. 90.
https://nsuworks.nova.edu/math_facarticles/90