An exact closed walks series formula for the complexity of regular graphs and some related bounds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918125223542784 |
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| author | Constantine, Gregory P Magda, Gregory |
| author_facet | Constantine, Gregory P Magda, Gregory |
| contents | The complexity of a graph is the number of its labeled spanning trees. In this work complexity is studied in settings that admit regular graphs. An exact formula is established linking complexity of the complement of a regular graph to numbers of closed walks in the graph by way of an infinite alternating series. Some consequences of this result yield infinite classes of lower and upper bounds on the complexity of such graphs. Applications of these mathematical results to biological problems on neuronal activity are described. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18019 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An exact closed walks series formula for the complexity of regular graphs and some related bounds Constantine, Gregory P Magda, Gregory Combinatorics The complexity of a graph is the number of its labeled spanning trees. In this work complexity is studied in settings that admit regular graphs. An exact formula is established linking complexity of the complement of a regular graph to numbers of closed walks in the graph by way of an infinite alternating series. Some consequences of this result yield infinite classes of lower and upper bounds on the complexity of such graphs. Applications of these mathematical results to biological problems on neuronal activity are described. |
| title | An exact closed walks series formula for the complexity of regular graphs and some related bounds |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2501.18019 |