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An endpoint exception to a conjectured equality characterization for Laplacian eigenvalue products
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.
Related
- Eigenvalue comparison theorems for the Witten-Laplacian and the weighted p-Laplacian on complete manifolds with a modified Ricci curvature bounded from below
- Sharp lower bound of the first eigenvalue of the p-Laplacian under integral Ricci curvature
- Eigenvalue Distribution of the Laplacian on Random Complexes
- Non-radial minimizers for the first eigenvalue of the Laplacian in cones and a related overdetermined problem
- The least signless Laplacian eigenvalue of {C3,C5}-free graphs
BibTeX
@misc{gibson2026endpoint,
title = {{An endpoint exception to a conjectured equality characterization for Laplacian eigenvalue products}},
author = {Scott Gibson},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16049},
eprint = {2609.16049},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16049},
}
RIS
TY - UNPB
TI - An endpoint exception to a conjectured equality characterization for Laplacian eigenvalue products
AU - Scott Gibson
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2609.16049
UR - https://arxiv.org/abs/2609.16049
AB - 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.
ER -