PreprintCC BY 4.0arXiv
Congruent quotient matrix, nodal domain, and nodal count
Abstract
We introduce the congruent quotient matrix along with its inequalities on inertia and demonstrate that these inequalities are the essence of the discrete nodal domain theorem, the bounds on nodal counts, and Fiedler's characterization on tree eigenvectors. Using these techniques, we also extend the existing bounds for the number of nodal domains and nodal counts.
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BibTeX
@misc{lin2026congruent,
title = {{Congruent quotient matrix, nodal domain, and nodal count}},
author = {Jephian C. -H. Lin},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00789},
eprint = {2611.00789},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00789},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Congruent quotient matrix, nodal domain, and nodal count
AU - Jephian C. -H. Lin
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00789
UR - https://arxiv.org/abs/2611.00789
AB - We introduce the congruent quotient matrix along with its inequalities on inertia and demonstrate that these inequalities are the essence of the discrete nodal domain theorem, the bounds on nodal counts, and Fiedler's characterization on tree eigenvectors. Using these techniques, we also extend the existing bounds for the number of nodal domains and nodal counts.
ER -