Let T be the multiplicative group of complex units, and let L (Φ) denote the Laplacian matrix of a nonempty T-gain graph Φ = (Γ, T, γ). The gain line graph L (Φ) and the gain subdivision graph S (Φ) are defined up to switching equivalence. We discuss how the eigenspaces determined by the adjacency eigenvalues of L (Φ) and S (Φ) are related with those of L (Φ)
