Department of Mathematics
On the second largest Laplacian eigenvalues of graphs
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. © 2012 Elsevier Inc. All rights reserved.
Graph, Laplacian separator, Second largest Laplacian eigenvalue
Source Publication Title
Linear Algebra and Its Applications
Li, Jianxi, Ji-Ming Guo, and Wai Chee Shiu. "On the second largest Laplacian eigenvalues of graphs." Linear Algebra and Its Applications 438.5 (2013): 2438-2446.