On the second largest Laplacian eigenvalues of graphs |
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| Authors: | Jianxi Li Ji-Ming Guo Wai Chee Shiu |
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| Affiliation: | 1. Department of Mathematics and Information Science, Zhangzhou Normal University, Zhangzhou, Fujian, PR China;2. Department of Applied Mathematics, China University of Petroleum, Dongying, Shandong, PR China;3. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, PR China |
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| 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. |
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