On the second largest Laplacian eigenvalue of trees | Synapse
September 10, 2025
On the second largest Laplacian eigenvalue of trees
Key Points
A complete characterization of trees with second largest laplacian eigenvalue at most 2+√3 was achieved.
Identifying trees that have exactly one laplacian eigenvalue exceeding 2+√3 provides crucial insights into their structure.
Insights into the second largest laplacian eigenvalue can enhance understanding of spectral graph theory.
Determining these properties has implications for applications in various graph-related fields.
Abstract
We determine all trees for which the second largest Laplacian eigenvalue is at most 2+3 as well as all trees with exactly one Laplacian eigenvalue exceeding 2+3.