10.46298/dmtcs.9432
https://dmtcs.episciences.org/9432
Dankelmann, Peter
Peter
Dankelmann
Mafunda, Sonwabile
Sonwabile
Mafunda
Mallu, Sufiyan
Sufiyan
Mallu
Proximity, remoteness and maximum degree in graphs
The average distance of a vertex $v$ of a connected graph $G$ is the
arithmetic mean of the distances from $v$ to all other vertices of $G$. The
proximity $\pi(G)$ and the remoteness $\rho(G)$ of $G$ are the minimum and the
maximum of the average distances of the vertices of $G$, respectively.
In this paper, we give upper bounds on the remoteness and proximity for
graphs of given order, minimum degree and maximum degree. Our bounds are sharp
apart from an additive constant.
Comment: 20 pages
episciences.org
Mathematics - Combinatorics
05C12
Attribution 4.0 International (CC BY 4.0)
2022-10-24
2022-11-30
2022-11-30
eng
journal article
arXiv:2201.09269
10.48550/arXiv.2201.09269
1365-8050
https://dmtcs.episciences.org/9432/pdf
VoR
application/pdf
Discrete Mathematics & Theoretical Computer Science
vol. 24, no 2
Graph Theory
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