A note on $k$-metric dimensional graphs

Abstract

Given a graph $G=(V,E)$, a set $S\subset V$ is called a $k$-\emph{metric generator} for $G$ if any pair of different vertices of $G$ is distinguished by at least $k$ elements of $S$. A graph is $k$-\emph{metric dimensional} if $k$ is the largest integer such that there exists a $k$-metric generator for $G$. This paper studies some bounds on the number $k$ for which a graph is $k$-metric dimensional.

11 pages, 3 figures

References in corpus (2)

• The k-metric dimension of graphs: a general approach
• On the complexity of computing the $k$-metric dimension of graphs

Cited by in corpus (1)

• Finite metric and $k$-metric bases on ultrametric spaces