Generalized Spectral Characterization of Signed Trees
Let $T$ be a tree with an irreducible characteristic polynomial $\phi(x)$ over $\mathbb{Q}$. Let $\Delta(T)$ be the discriminant of $\phi(x)$. It is proved that if $2^{-\frac n2}\sqrt{\Delta(T)}$ (which is always an integer) is odd and square free, then every signed tree with underlying graph $T$ is determined by its generalized spectrum.
Authors
- Yizhe Ji (ORCID: https://orcid.org/0000-0002-5865-394X)
- Hao Zhang (ORCID: https://orcid.org/0009-0009-7008-6712)
- Wei Wang (ORCID: https://orcid.org/0009-0001-2974-3591)
Publication Details
- Journal
- The Electronic Journal of Combinatorics
- Published
- 2025-04-24
- DOI
- https://doi.org/10.37236/12423
- Citations
- 3
- Primary Topic
- Graph theory and applications
- Type
- article
- Field-Weighted Citation Impact
- 12.26
Funders
- National Natural Science Foundation of China
- East China University of Science and Technology
- Natural Science Foundation of Hunan Province
- National Key Research and Development Program of China
- Fundamental Research Funds for the Central Universities