On the extreme complexity of certain nearly regular graphs
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915145344614400 |
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| author | Constantine, Gregory P Magda, Gregory C |
| author_facet | Constantine, Gregory P Magda, Gregory C |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06886 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the extreme complexity of certain nearly regular graphs Constantine, Gregory P Magda, Gregory C Combinatorics 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. |
| title | On the extreme complexity of certain nearly regular graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2502.06886 |