Proximity in triangulations and quadrangulations
| Autor: | Czabarka, Éva, Dankelmann, Peter, Olsen, Trevor, Székely, László A. |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Electronic Journal of Graph Theory and Applications. 10:425 |
| ISSN: | 2338-2287 |
| DOI: | 10.5614/ejgta.2022.10.2.7 |
| Popis: | Let $ G $ be a connected graph. If $\bar{\sigma}(v)$ denotes the arithmetic mean of the distances from $v$ to all other vertices of $G$, then the proximity, $\pi(G)$, of $G$ is defined as the smallest value of $\bar{\sigma}(v)$ over all vertices $v$ of $G$. We give upper bounds for the proximity of simple triangulations and quadrangulations of given order and connectivity. We also construct simple triangulations and quadrangulations of given order and connectivity that match the upper bounds asymptotically and are likely optimal. Comment: arXiv admin note: text overlap with arXiv:1905.06753 |
| Databáze: | OpenAIRE |
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