On the null space struture associted with trees and cycles
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.