Threshold graphs are characterized by sharing a common integer Laplacian eigenbasis across all graphs of the same order, and this note supplies a new proof of the characterization.
Merris,Graph theory, Wiley-Interscience Series in Discrete Mathe- matics and Optimization, Wiley-Interscience, New York
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A Note on the Laplacian Eigenvectors of Threshold Graphs
Threshold graphs are characterized by sharing a common integer Laplacian eigenbasis across all graphs of the same order, and this note supplies a new proof of the characterization.