Bounds on the eigenvalues of graphs with cut vertices or edges |
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Authors: | Bao-Xuan Zhu |
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Affiliation: | School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, PR China |
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Abstract: | In this paper, we characterize the extremal graph having the maximal Laplacian spectral radius among the connected bipartite graphs with n vertices and k cut vertices, and describe the extremal graph having the minimal least eigenvalue of the adjacency matrices of all the connected graphs with n vertices and k cut edges. We also present lower bounds on the least eigenvalue in terms of the number of cut vertices or cut edges and upper bounds on the Laplacian spectral radius in terms of the number of cut vertices. |
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Keywords: | 05C50 15A18 |
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