OpenAlex ·
An endpoint exception to a conjectured equality characterization for Laplacian eigenvalue products
- Published
- Source
- OpenAlex
- Published in
- arXiv (Cornell University)
- DOI
- 10.48550/arxiv.2609.16049
- Original
- Read it at the publisher
- Topics
Abstract
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 complement are connected. These examples do not contradict the numerical inequality in that conjecture.
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