Geodesic
Proximity, remoteness and maximum degree in graphs
Discrete mathematics & theoretical computer science, Tome 24 (2022) no. 2.

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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.
DOI : 10.46298/dmtcs.9432
Classification : 05C12, 05C35, 05C38 
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Dankelmann, Peter; Mafunda, Sonwabile; Mallu, Sufiyan. Proximity, remoteness and maximum degree in graphs. Discrete mathematics & theoretical computer science, Tome 24 (2022) no. 2. doi : 10.46298/dmtcs.9432. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.9432/

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