eng
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
2022-11-30
vol. 24, no 2
Graph Theory
10.46298/dmtcs.9432
9432
journal article
Proximity, remoteness and maximum degree in graphs
Peter Dankelmann
Sonwabile Mafunda
Sufiyan Mallu
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.
https://dmtcs.episciences.org/9432/pdf
Mathematics - Combinatorics
05C12