Generalized spectral characterization of signed bipartite graphs

Abstract

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.