Generalized spectral characterization of signed bipartite graphs
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915291869478912 |
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| author | Guo, Songlin Wang, Wei Li, Lele |
| author_facet | Guo, Songlin Wang, Wei Li, Lele |
| contents | Let $Σ$ be an $n$-vertex controllable or almost controllable signed bipartite graph, and let $Δ_Σ$ denote the discriminant of its characteristic polynomial $χ(Σ; x)$. We prove that if (\rmnum{1}) the integer $2^{ -\lfloor n/2 \rfloor }\sqrt{Δ_Σ}$ is squarefree, and (\rmnum{2}) the constant term (even $n$) or linear coefficient (odd $n$) of $χ(Σ; x)$ is $\pm 1$, then $Σ$ is determined by its generalized spectrum. This result extends a recent theorem of Ji, Wang, and Zhang [Electron. J. Combin. 32 (2025), \#P2.18], which established a similar criterion for signed trees with irreducible characteristic polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12446 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized spectral characterization of signed bipartite graphs Guo, Songlin Wang, Wei Li, Lele Combinatorics Let $Σ$ be an $n$-vertex controllable or almost controllable signed bipartite graph, and let $Δ_Σ$ denote the discriminant of its characteristic polynomial $χ(Σ; x)$. We prove that if (\rmnum{1}) the integer $2^{ -\lfloor n/2 \rfloor }\sqrt{Δ_Σ}$ is squarefree, and (\rmnum{2}) the constant term (even $n$) or linear coefficient (odd $n$) of $χ(Σ; x)$ is $\pm 1$, then $Σ$ is determined by its generalized spectrum. This result extends a recent theorem of Ji, Wang, and Zhang [Electron. J. Combin. 32 (2025), \#P2.18], which established a similar criterion for signed trees with irreducible characteristic polynomials. |
| title | Generalized spectral characterization of signed bipartite graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2505.12446 |