The inverse nullity pair problem and the strong nullity interlacing property
Combinatorics
2023-10-24 v1
Abstract
The inverse eigenvalue problem studies the possible spectra among matrices whose off-diagonal entries have their zero-nonzero patterns described by the adjacency of a graph . In this paper, we refer to the -nullity pair of a matrix as , where is the matrix obtained from by removing the -th row and column. The inverse -nullity pair problem is considered for complete graphs, cycles, and trees. The strong nullity interlacing property is introduced, and the corresponding supergraph lemma and decontraction lemma are developed as new tools for constructing matrices with a given nullity pair.
Cite
@article{arxiv.2310.13884,
title = {The inverse nullity pair problem and the strong nullity interlacing property},
author = {Aida Abiad and Bryan A. Curtis and Mary Flagg and H. Tracy Hall and Jephian C. -H. Lin and Bryan Shader},
journal= {arXiv preprint arXiv:2310.13884},
year = {2023}
}