Generalized spectral characterization of signed trees

2023/10/02 by Yizhe Ji, Wei Wang, Ji, Yizhe +3 · 1 citation
Chemistry · Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.2310.00846

openalex publication_date 2023/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let T be a tree with an irreducible characteristic polynomial ϕ(x) over ℚ. Let Δ(T) be the discriminant of ϕ(x). It is proved that if 2^{-\frac n2}√(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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