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- W2396504703 abstract "Let $(X,d)$ be a metric space. A set $Ssubseteq X$ is said to be a $k$-metric generator for $X$ if and only if for any pair of different points $u,vin X$, there exist at least $k$ points $w_1,w_2, ldots w_kin S$ such that $d(u,w_i)ne d(v,w_i),; mbox{rm for all}; iin {1, ldots k}.$ Let $mathcal{R}_k(X)$ be the set of metric generators for $X$. The $k$-metric dimension $dim_k(X)$ of $(X,d)$ is defined as $$dim_k(X)=inf{|S|:, Sin mathcal{R}_k(X)}.$$ Here, we discuss the $k$-metric dimension of $(V,d_t)$, where $V$ is the set of vertices of a simple graph $G$ and the metric $d_t:Vtimes Vrightarrow mathbb{N}cup {0}$ is defined by $d_t(x,y)=min{d(x,y),t}$ from the geodesic distance $d$ in $G$ and a positive integer $t$. The case $tge D(G)$, where $D(G)$ denotes the diameter of $G$, corresponds to the original theory of $k$-metric dimension and the case $t=2$ corresponds to the theory of $k$-adjacency dimension. Furthermore, this approach allows us to extend the theory of $k$-metric dimension to the general case of non-necessarily connected graphs." @default.
- W2396504703 created "2016-06-24" @default.
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- W2396504703 date "2016-05-21" @default.
- W2396504703 modified "2023-10-14" @default.
- W2396504703 title "The k-metric dimension of graphs: a general approach" @default.
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- W2396504703 doi "https://doi.org/10.48550/arxiv.1605.06709" @default.
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