Average eccentricity, \(k\)-packing and \(k\)-domination in graphs
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.
scientific article; zbMATH DE number 7041383