Peter Dankelmann ; Sonwabile Mafunda ; Sufiyan Mallu - Proximity, remoteness and maximum degree in graphs

dmtcs:9432 - Discrete Mathematics & Theoretical Computer Science, November 30, 2022, vol. 24, no 2 - https://doi.org/10.46298/dmtcs.9432
Proximity, remoteness and maximum degree in graphsArticle

Authors: 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.

    Comment: 20 pages

    https://doi.org/10.46298/dmtcs.9432
    Source: arXiv.org:2201.09269
    Volume: vol. 24, no 2
    Section: Graph Theory
    Published on: November 30, 2022
    Accepted on: October 24, 2022
    Submitted on: May 6, 2022
    Keywords: Mathematics - Combinatorics, 05C12
    Licence: Attribution 4.0 International (CC BY 4.0)

    Classifications

    Mathematics Subject Classification 20201
    Sources:
    • [1] zbMATH Open.

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