Minimizing the determinant of the graph Laplacian
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911833033539584 |
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| author | Albin, Nathan Lind, Joan Melikyan, Anna Poggi-Corradini, Pietro |
| author_facet | Albin, Nathan Lind, Joan Melikyan, Anna Poggi-Corradini, Pietro |
| contents | In this paper, we study extremal values for the determinant of the weighted graph Laplacian under simple nondegeneracy conditions on the weights. We derive necessary and sufficient conditions for the determinant of the Laplacian to be bounded away from zero and for the existence of a minimizing set of weights. These conditions are given both in terms of properties of random spanning trees and in terms of a type of density on graphs. These results generalize and extend the work of [7]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_06363 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimizing the determinant of the graph Laplacian Albin, Nathan Lind, Joan Melikyan, Anna Poggi-Corradini, Pietro Combinatorics Optimization and Control 90C27 (Primary), 05B35 (Secondary) In this paper, we study extremal values for the determinant of the weighted graph Laplacian under simple nondegeneracy conditions on the weights. We derive necessary and sufficient conditions for the determinant of the Laplacian to be bounded away from zero and for the existence of a minimizing set of weights. These conditions are given both in terms of properties of random spanning trees and in terms of a type of density on graphs. These results generalize and extend the work of [7]. |
| title | Minimizing the determinant of the graph Laplacian |
| topic | Combinatorics Optimization and Control 90C27 (Primary), 05B35 (Secondary) |
| url | https://arxiv.org/abs/2404.06363 |