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arXiv · 2611.00789

Congruent quotient matrix, nodal domain, and nodal count

Jephian C. -H. Lin
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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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Jephian C. -H. Lin. 2026-10-31. Congruent quotient matrix, nodal domain, and nodal count. https://arxiv.org/abs/2611.00789

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