Abstract
The second largest Laplacian eigenvalue of a graph is the second largest eigenvalue of the associated Laplacian matrix. In this paper, we study extremal graphs for the extremal values of the second largest Laplacian eigenvalue and the Laplacian separator of a connected graph, respectively. All simple connected graphs with second largest Laplacian eigenvalue at most 3 are characterized. It is also shown that graphs with second largest Laplacian eigenvalue at most 3 are determined by their Laplacian spectrum. Moreover, the graphs with maximum and the second maximum Laplacian separators among all connected graphs are determined.
Original language | English |
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Pages (from-to) | 2438-2446 |
Number of pages | 9 |
Journal | Linear Algebra and Its Applications |
Volume | 438 |
Issue number | 5 |
DOIs | |
Publication status | Published - 1 Mar 2013 |
Scopus Subject Areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics
User-Defined Keywords
- Graph
- Laplacian separator
- Second largest Laplacian eigenvalue