An endpoint exception to a conjectured equality characterization for Laplacian eigenvalue products
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Gibson, Scott
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213429954