Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2405.15058 |
| Tags: |
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Inhaltsangabe:
- Let $G$ be a finite, simple connected graph. The average distance of a vertex $v$ of $G$ is the arithmetic mean of the distances from $v$ to all other vertices of $G$. The remoteness $ρ(G)$ of $G$ is the maximum of the average distances of the vertices of $G$. In this paper, we give sharp upper bounds on the remoteness of a graph of given order, connectivity and size. We also obtain corresponding bound s for $2$-edge-connected and $3$-edge-connected graphs, and bounds in terms of order and size for triangle-free graphs.