Remoteness of graphs with given size and connectivity constraints
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909209905332224 |
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| author | Dankelmann, Peter Mafunda, Sonwabile Mallu, Sufiyan |
| author_facet | Dankelmann, Peter Mafunda, Sonwabile Mallu, Sufiyan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_15058 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Remoteness of graphs with given size and connectivity constraints Dankelmann, Peter Mafunda, Sonwabile Mallu, Sufiyan Combinatorics 05C12 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. |
| title | Remoteness of graphs with given size and connectivity constraints |
| topic | Combinatorics 05C12 |
| url | https://arxiv.org/abs/2405.15058 |