Bounds on normalized Laplacian eigenvalues of graphs. (English) Zbl 1332.05090
Summary: Let \(G\) be a simple connected graph of order \(n\), where \(n \geq 2\). Its normalized Laplacian eigenvalues are \(0 = \lambda_1 \leq \lambda_2 \leq \dots \leq \lambda _n \leq 2\). In this paper, some new upper and lower bounds on \(\lambda_n\) are obtained, respectively. Moreover, connected graphs with \(\lambda_n\) (or \(\lambda_{n-1}=1\)) are also characterized.
MSC:
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
| 15A18 | Eigenvalues, singular values, and eigenvectors |
| 05C40 | Connectivity |
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