Journal of Mathematics, Volume (2022), No (1), Year (2022-9) , Pages (1-6)

Title : ( Metric Dimension Threshold of Graphs )

Authors: Meysam Korivand , Kazem Khashyarmanesh , Mostafa Tavakoli ,

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‎Let $G$ be a connected graph‎. ‎A subset $S$ of vertices of $G$ is said to be a resolving set of $G$‎, ‎if for any two vertices $u$‎ ‎and $v$ of $G$ there is at least a member $w$ of $S$ such that $\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\T{d}(u‎, ‎w) \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\neq \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\T{d}(v‎, ‎w)$‎. ‎The minimum number‎ ‎$t$ that any subset $S$ of vertices $G$ with $\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\vert S \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\vert =t$ is a resolving set for $G$‎, ‎is called the metric dimension threshold and is denoted by $\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\T{dim}_{th}(G)$‎. ‎In this paper‎, ‎the concept of metric dimension threshold is introduced according to its application in some real word problems‎. ‎Also‎, ‎the metric dimension threshold of some families of graphs and a characterization of graphs‎ ‎$G$ of order $n$ for which the metric dimension threshold equals $2$‎, ‎$n-2$‎, ‎and $n-1$‎, ‎are given‎. ‎Moreover‎, ‎some graphs with equal the metric dimension threshold and the standard metric dimension of graphs are presented‎.


, Graph, metric dimension threshold.
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author = {Korivand, Meysam and Khashyarmanesh, Kazem and Tavakoli, Mostafa},
title = {Metric Dimension Threshold of Graphs},
journal = {Journal of Mathematics},
year = {2022},
volume = {2022},
number = {1},
month = {September},
issn = {2314-4629},
pages = {1--6},
numpages = {5},
keywords = {Graph; metric dimension threshold.},


%0 Journal Article
%T Metric Dimension Threshold of Graphs
%A Korivand, Meysam
%A Khashyarmanesh, Kazem
%A Tavakoli, Mostafa
%J Journal of Mathematics
%@ 2314-4629
%D 2022