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An endpoint exception to a conjectured equality characterization for Laplacian eigenvalue products
We give eight-vertex counterexamples to the equality characterization in Conjecture 20 of Chen, Guo, Li and Wang, Electron. J. Combin. 32(4) (2025), P4.37. The examples occur at the included endpoint $k=3n/4$ and extend to infinite families, including a family for which both the graph and its comple
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