Generalized spectral characterization of signed bipartite graphs

Let $\mathrm{\Sigma }$ be an $n$-vertex controllable or almost controllable signed bipartite graph, and let ${\mathrm{\Delta }}_{\mathrm{\Sigma }}$ denote the discriminant of its characteristic polynomial $\chi (\mathrm{\Sigma };x)$. We prove that if (\rmnum{1}) the integer $2^{-\lfloor n\mathrm{/}2\rfloor }\sqrt{{\mathrm{\Delta }}_{\mathrm{\Sigma }}}$ is squarefree, and (\rmnum{2}) the constant term (even $n$) or linear coefficient (odd $n$) of $\chi (\mathrm{\Sigma };x)$ is $\pm 1$, then $\mathrm{\Sigma }$ 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.