Average eccentricity, \(k\)-packing and \(k\)-domination in graphs
type: Item
instance of: scholarly article
title: Average eccentricity, \(k\)-packing and \(k\)-domination in graphs
zbMATH Open document ID: 1415.05044
author: Peter Dankelmann
author: F. J. Osaye
published in: Discrete Mathematics
publication date: 2019-03-25T00:00:00Z
review text: Let $G$ be a connected graph. The eccentricity $e(v)$ of a vertex $v$ is the distance from $v$ to a vertex farthest from $v$. The average eccentricity avec($G$) of $G$ is defined as the average of the eccentricities of the vertices of $G$. For $k \in \mathbb{N} $, the $k$-packing number of $G$ is the largest cardinality of a set of vertices of $G$ whose pairwise distance is greater than $k$. A $k$-dominating set of $G$ is a set $S$ of vertices such that every vertex of $G$ is within distance $k$ from some vertex of $S$. The $k$-domination number (connected $k$-domination number) of $G$ is the minimum cardinality of a $k$-dominating set (of a $k$-dominating set that induces a connected subgraph) of $G$. This paper generalises the results on the maximum value of the average eccentricity of graphs with given order and domination number and independence number which is already in the literature.
Mathematics Subject Classification ID: 05C12
Mathematics Subject Classification ID: 05C69
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C40
zbMATH DE Number: 7041383
zbMATH Keywords: eccentricity
zbMATH Keywords: average eccentricity
zbMATH Keywords: total eccentricity
zbMATH Keywords: packing number
zbMATH Keywords: independence number
zbMATH Keywords: domination number
reviewed by: G. N. Prasanth
MaRDI profile type: Publication
full work available at URL: j.disc.2019.01.004
OpenAlex ID: W2912256696
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DOI: 10.1016/J.DISC.2019.01.004
description: scientific article; zbMATH DE number 7041383