The coherent rank of a graph with three eigenvalues
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929399407837184 |
|---|---|
| author | Greaves, Gary Yip, Jose |
| author_facet | Greaves, Gary Yip, Jose |
| contents | We characterise graphs that have three distinct eigenvalues and coherent ranks 8 and 9, linking the former to certain symmetric 2-designs and the latter to specific quasi-symmetric 2-designs. This characterisation leads to the discovery of a new biregular graph with three distinct eigenvalues. Additionally, we demonstrate that the coherent rank of a triregular graph with three distinct eigenvalues is at least 14. Finally, we introduce a conjecturally infinite family of biregular graphs with three distinct eigenvalues, obtained by switching the block graphs of orthogonal arrays. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17395 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The coherent rank of a graph with three eigenvalues Greaves, Gary Yip, Jose Combinatorics We characterise graphs that have three distinct eigenvalues and coherent ranks 8 and 9, linking the former to certain symmetric 2-designs and the latter to specific quasi-symmetric 2-designs. This characterisation leads to the discovery of a new biregular graph with three distinct eigenvalues. Additionally, we demonstrate that the coherent rank of a triregular graph with three distinct eigenvalues is at least 14. Finally, we introduce a conjecturally infinite family of biregular graphs with three distinct eigenvalues, obtained by switching the block graphs of orthogonal arrays. |
| title | The coherent rank of a graph with three eigenvalues |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2406.17395 |