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Bounds on the Multiplicity of Eigenvalues for Fixed Membranes

✍ Scribed by T. Hoffmann-Ostenhof; P. W. Michor; N. Nadirashvili


Publisher
Springer
Year
1999
Tongue
English
Weight
211 KB
Volume
9
Category
Article
ISSN
1016-443X

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Sharp bounds on the eigenvalues of trees
✍ Shengbiao Hu πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 289 KB

Let Ξ» 1 (T ) and Ξ» 2 (T ) be the largest and the second largest eigenvalues of a tree T , respectively. We obtain the following sharp lower bound for Ξ» 1 (T ): where d i is the degree of the vertex v i and m i is the average degree of the adjacent vertices of v i . Equality holds if and only if T i