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arXiv · 2310.00846

Generalized spectral characterization of signed trees

Yizhe Ji·Wei Wang·Hao Zhang
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Abstract

Let $T$ be a tree with an irreducible characteristic polynomial $ϕ(x)$ over $\mathbb{Q}$. Let $Δ(T)$ be the discriminant of $ϕ(x)$. It is proved that if $2^{-\frac n2}\sqrt{Δ(T)}$ (which is always an integer) is odd and square free, then every signed tree with underlying graph $T$ is determined by its generalized spectrum.

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Yizhe Ji, Wei Wang, Hao Zhang. 2023-10-02. Generalized spectral characterization of signed trees. https://arxiv.org/abs/2310.00846

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