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• W3022755142 abstract "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 $d(u,w_i)ne d(v,w_i),; textrm{for all}; iin {1, ldots k}.$ 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 $$begin{equation*}dim_k(X)=inf{|S|:, Sin mathcal{R}_k(X)}.end{equation*}$$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. Finally, we analyse the computational complexity of determining the $k$-metric dimension of $(V,d_t)$ for the metric $d_t$." @default.
• W3022755142 created "2020-05-13" @default.
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• W3022755142 date "2020-04-08" @default.
• W3022755142 modified "2023-09-25" @default.
• W3022755142 title "On The (<i>k,t</i>)-Metric Dimension Of Graphs" @default.
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• W3022755142 doi "https://doi.org/10.1093/comjnl/bxaa009" @default.
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