This note demonstrates eigenvalue conditions in gain graphs, suggesting new lower energy bounds.
Let ? = (G, ?) be a T-gain graph. In this note we show that ? has one positive and negative eigenvalues if and only if it is switching equivalent to a balanced complete bipartite graph or complete tripartite with special weights. In addition, we found some lower bounds for the energy of a T-gain graph.
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Adish et al. (2025) studied this question.
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