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Line graphs with exactly two positive eigenvalues. (English) Zbl 1052.05046

The set of connected line graphs whose third largest eigenvalue does not exceed 0 is characterized in two ways: by maximal graphs having this property and by minimal forbidden induced subgraphs for the same property. In addition, line graphs with exactly two positive eigenvalues are characterized.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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