Geodesic
Generalized spectral characterization of signed trees
The electronic journal of combinatorics, Tome 32 (2025) no. 2
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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.
DOI : 10.37236/12423
Classification : 05C50, 05C22
Mots-clés : spectra, trees, signed graph, spectral graphs 
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     author = {Yizhe Ji and Wei Wang and Hao Zhang},
     title = {Generalized spectral characterization of signed trees},
     journal = {The electronic journal of combinatorics},
     year = {2025},
     volume = {32},
     number = {2},
     doi = {10.37236/12423},
     zbl = {1564.05195},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/12423/}
}
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Yizhe Ji; Wei Wang; Hao Zhang. Generalized spectral characterization of signed trees. The electronic journal of combinatorics, Tome 32 (2025) no. 2. doi: 10.37236/12423

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