Solution to an open problem on Laplacian ratio
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914692027383808 |
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| author | Wu, T. |
| author_facet | Wu, T. |
| contents | Let G be a graph. The Laplacian ratio of G is the permanent of the Laplacian matrix of G divided by the product of degrees of all vertices. The computational complexity of Laplacian ratio is #P-complete. Brualdi and Goldwasser studied systematicly the properties of Laplacian ratios of graphs. And they proposed an open problem: what is the minimum value of the Laplacian ratios of trees with n vertices having diameter at least k ? In this paper, we give a solution to the problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15669 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solution to an open problem on Laplacian ratio Wu, T. Combinatorics Let G be a graph. The Laplacian ratio of G is the permanent of the Laplacian matrix of G divided by the product of degrees of all vertices. The computational complexity of Laplacian ratio is #P-complete. Brualdi and Goldwasser studied systematicly the properties of Laplacian ratios of graphs. And they proposed an open problem: what is the minimum value of the Laplacian ratios of trees with n vertices having diameter at least k ? In this paper, we give a solution to the problem. |
| title | Solution to an open problem on Laplacian ratio |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2402.15669 |