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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.02179 |
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| _version_ | 1866929611737137152 |
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| author | Gomyou, Takumi Nayatani, Shin |
| author_facet | Gomyou, Takumi Nayatani, Shin |
| contents | Given a length function on the set of edges of a finite graph, the corresponding Fujiwara Laplacian is defined. We consider a problem of maximizing the first nonzero eigenvalue of this graph Laplacian over all choices of edge-length function subject to a certain normalization. In this paper we prove that the supremum of the first nonzero eigenvalue is infinite whenever the graph contains a cycle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02179 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximization of the first Laplace eigenvalue of a finite graph II Gomyou, Takumi Nayatani, Shin Combinatorics 05C62 (Primary) 05C50 (Secondary) Given a length function on the set of edges of a finite graph, the corresponding Fujiwara Laplacian is defined. We consider a problem of maximizing the first nonzero eigenvalue of this graph Laplacian over all choices of edge-length function subject to a certain normalization. In this paper we prove that the supremum of the first nonzero eigenvalue is infinite whenever the graph contains a cycle. |
| title | Maximization of the first Laplace eigenvalue of a finite graph II |
| topic | Combinatorics 05C62 (Primary) 05C50 (Secondary) |
| url | https://arxiv.org/abs/2412.02179 |