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Bounds on the eigenvalues of graphs with cut vertices or edges

โœ Scribed by Bao-Xuan Zhu

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
325 KB
Volume
434
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

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.

๐Ÿ“œ SIMILAR VOLUMES

On the signless Laplacian spectral radiu
On the signless Laplacian spectral radius of graphs with cut vertices
โœ Bao-Xuan Zhu ๐Ÿ“‚ Article ๐Ÿ“… 2010 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 129 KB

In this paper, we show that among all the connected graphs with n vertices and k cut vertices, the maximal signless Laplacian spectral radius is attained uniquely at the graph G n,k , where G n,k is obtained from the complete graph K n-k by attaching paths of almost equal lengths to all vertices of