The smallest normalized signless $\infty$-Laplacian eigenvalue for non-bipartite connected graphs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916545412726784 |
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| author | Dai, Yi |
| author_facet | Dai, Yi |
| contents | In this paper, we aim to study the smallest normalized signless $\infty$-Laplacian eigenvalue $μ_{\infty}$, a generalisation of the smallest signless Laplacian eigenvalue. For a non-bipartite connected graph, we show that the invariant $μ_{\infty}$ equals to the reciprocal of the minimal $\infty$-norm of the generalized inverses of the weighted signless incidence matrix. An example is also given to illustrate the result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20513 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The smallest normalized signless $\infty$-Laplacian eigenvalue for non-bipartite connected graphs Dai, Yi Combinatorics In this paper, we aim to study the smallest normalized signless $\infty$-Laplacian eigenvalue $μ_{\infty}$, a generalisation of the smallest signless Laplacian eigenvalue. For a non-bipartite connected graph, we show that the invariant $μ_{\infty}$ equals to the reciprocal of the minimal $\infty$-norm of the generalized inverses of the weighted signless incidence matrix. An example is also given to illustrate the result. |
| title | The smallest normalized signless $\infty$-Laplacian eigenvalue for non-bipartite connected graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2412.20513 |