arXiv
Open Access
2016
Eigenvalue estimates on quantum graphs
Sinan Ariturk
Abstrak
On a finite connected metric graph, we establish upper bounds for the eigenvalues of the Laplacian. These bounds depend on the length, the Betti number, and the number of pendant vertices. For trees, these estimates are sharp. We also establish sharp upper bounds for the spectral gap of the complete graph $K_4$. The proofs are based on estimates for eigenvalues on graphs with Dirichlet conditions imposed at the pendant vertices.
Penulis (1)
S
Sinan Ariturk
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2016
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- en
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- arXiv
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- Open Access ✓