In this paper, we provide the smallest value of the second largest Laplacian eigenvalue for any unicyclic graph, and find the unicyclic graphs attaining that value. And also give an “asymptotically good” upper bounds for the second largest Laplacian eigenvalues of unicyclic graphs. Using this results, we can determine unicyclic graphs with maximum Laplacian separator. And unicyclic graphs with maximum Laplacian spread will also be determined. Copyright © 2008 Elsevier Inc. All rights reserved.
CitationLi, J., Shiu, W. C., & Chan, W. H. (2009). Some results on the Laplacian eigenvalues of unicyclic graphs. Linear Algebra and Its Applications, 430(8-9), 2080-2093. doi: 10.1016/j.laa.2008.11.016
- Unicyclic graphs
- Laplacian eigenvalues
- Laplacian separator
- Laplacian spread