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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.17395 |
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Table of 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.