Generalized spectral characterization of signed bipartite graphs

Abstract

Let Σ be an n-vertex controllable or almost controllable signed bipartite graph, and let ${\Delta }_{\Sigma }$ denote the discriminant of its characteristic polynomial $\chi (\Sigma ;x)$. We prove that if (i) the integer $2^{-\lfloor n/2\rfloor }\sqrt{{\Delta }_{\Sigma }}$ is squarefree, and (ii) the constant term (even n) or linear coefficient (odd n) of $\chi (\Sigma ;x)$ is ±1, then Σ is determined by its generalized spectrum. This result extends a recent theorem of Ji et al. (2025) [6], which established a similar criterion for signed trees with irreducible characteristic polynomials.