On the robustness of the metric dimension of grid graphs to adding a single edge

@article{Mashkaria2022OnTR,
  title={On the robustness of the metric dimension of grid graphs to adding a single edge},
  author={Satvik Mashkaria and Gergely {\'O}dor and Patrick Thiran},
  journal={Discret. Appl. Math.},
  year={2022},
  volume={316},
  pages={1-27}
}

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References

SHOWING 1-10 OF 48 REFERENCES
Sequential metric dimension for random graphs
TLDR
This work finds that, in connected Erdős–Rényi graphs, the MD and the SMD are a constant factor apart, and shows that a strategy that greedily minimizes the number of candidate targets in each step uses asymptotically optimal queries in Erd� Hungarian graphs.
The effect of vertex or edge deletion on the metric dimension of graphs
The metric dimension dim(G) of a graph G is the minimum cardinality of a set of vertices such that every vertex of G is uniquely determined by its vector of distances to the chosen vertices. Let v
On Metric Generators of Graphs
TLDR
Results on the detection of false coins are used to approximate the metric dimension (minimum size of a generator for the metric space defined by the distances) of some particular graphs for which the problem was known and open and the existence of connected joins in graphs can be solved in polynomial time.
Resolvability in graphs and the metric dimension of a graph
Extremal results for graphs of bounded metric dimension
A comparison between the metric dimension and zero forcing number of trees and unicyclic graphs
The metric dimension dim(G) of a graph G is the minimum number of vertices such that every vertex of G is uniquely determined by its vector of distances to the chosen vertices. The zero forcing
On the metric dimension of HDN 3 and PHDN 3
  • F. Simon Raj, A. George
  • Mathematics
    2017 IEEE International Conference on Power, Control, Signals and Instrumentation Engineering (ICPCSI)
  • 2017
Let M = {m1, m2,…, mp} be an ordered set of vertices in a graph G(V, E). Then (d(u, m1), d(u, m2),…, d(u, mp)) is called the p-dimensional vector of distances coordinate or p-coordinate of a vertex u
The difference between the metric dimension and the determining number of a graph
Landmarks in torus networks
TLDR
It is proved that for torus TR(m, n), m≤n, the minimum metric dimension is 3 when at least one of m or n is odd and an upper bound is provided for theminimum metric dimension when both m and n are even.
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