Wei Wang

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math.CO2025

Generalized spectral characterization of signed bipartite graphs

Songlin Guo, Wei Wang, Lele Li

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…

math.CO2025

Primary decomposition theorem and generalized spectral characterization of graphs

Songlin Guo, Wei Wang

Suppose $G$ is a controllable graph of order $n$ with adjacency matrix $A$ . Let $W = [e, A e, \dots, A^{n - 1} e]$ ( $e$ is the all-one vector) and $Δ = \prod_{i > j} (α_{i} - α_{j})^{2}$ ( $α_{i}$ 's are e…