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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2502.06886 |
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Table des matières:
- The complexity of a graph is the number of its labeled spanning trees. It is demonstrated that the seven known triangle-free strongly regular graphs, such as the Higman-Sims graph, are graphs of maximal complexity among all graphs of the same order and degree; their complements are shown to be of minimal complexity. A generalization to nearly regular graphs with two distinct eigevalues of the Laplacian is presented. Conjectures and applications of these results to biological problems on neuronal activity are described.