Inverse eigenvalue problem for Laplacian matrices of a graph
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915041678196736 |
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| author | Fallat, Shaun Gupta, Himanshu Lin, Jephian C. -H. |
| author_facet | Fallat, Shaun Gupta, Himanshu Lin, Jephian C. -H. |
| contents | For a given graph $G$, we aim to determine the possible realizable spectra for a generalized (or sometimes referred to as a weighted) Laplacian matrix associated with $G$. This new specialized inverse eigenvalue problem is considered for certain families of graphs and graphs on a small number of vertices. Related considerations include studying the possible ordered multiplicity lists associated with stars and complete graphs and graphs with a few vertices. Finally, we present a novel investigation, both theoretically and numerically, the minimum variance over a family of generalized Laplacian matrices with a size-normalized weighting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00292 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inverse eigenvalue problem for Laplacian matrices of a graph Fallat, Shaun Gupta, Himanshu Lin, Jephian C. -H. Combinatorics 05C50, 15A18, 15B57, 65F18 For a given graph $G$, we aim to determine the possible realizable spectra for a generalized (or sometimes referred to as a weighted) Laplacian matrix associated with $G$. This new specialized inverse eigenvalue problem is considered for certain families of graphs and graphs on a small number of vertices. Related considerations include studying the possible ordered multiplicity lists associated with stars and complete graphs and graphs with a few vertices. Finally, we present a novel investigation, both theoretically and numerically, the minimum variance over a family of generalized Laplacian matrices with a size-normalized weighting. |
| title | Inverse eigenvalue problem for Laplacian matrices of a graph |
| topic | Combinatorics 05C50, 15A18, 15B57, 65F18 |
| url | https://arxiv.org/abs/2411.00292 |