Graph Laplacians with Higher Accuracy
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908306532990976 |
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| author | Yoon, Mary |
| author_facet | Yoon, Mary |
| contents | Motivated by discrete Laplacian differential operators with various accuracy orders in numerical analysis, we introduce new matrices attached to a simple graph that can be considered graph Laplacians with higher accuracy. In particular, we show that the number of graphs having cospectral mates with these matrices is significantly less than the ones with other known matrices. We also investigate their spectral properties and explicitly compute their eigenvalues and eigenvectors for some graphs. Along the line, we also prove the existence of a weighted signed graph with given Laplacian eigenvalues. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04461 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Graph Laplacians with Higher Accuracy Yoon, Mary Combinatorics 05C50, 05C22, 15A18, 15B99 Motivated by discrete Laplacian differential operators with various accuracy orders in numerical analysis, we introduce new matrices attached to a simple graph that can be considered graph Laplacians with higher accuracy. In particular, we show that the number of graphs having cospectral mates with these matrices is significantly less than the ones with other known matrices. We also investigate their spectral properties and explicitly compute their eigenvalues and eigenvectors for some graphs. Along the line, we also prove the existence of a weighted signed graph with given Laplacian eigenvalues. |
| title | Graph Laplacians with Higher Accuracy |
| topic | Combinatorics 05C50, 05C22, 15A18, 15B99 |
| url | https://arxiv.org/abs/2504.04461 |