# On the metric dimension of Cartesian powers of a graph

@article{Jiang2019OnTM, title={On the metric dimension of Cartesian powers of a graph}, author={Zilin Jiang and N. Polyanskii}, journal={J. Comb. Theory, Ser. A}, year={2019}, volume={165}, pages={1-14} }

Abstract A set of vertices S resolves a graph if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of a graph is the minimum cardinality of a resolving set of the graph. Fix a connected graph G on q ≥ 2 vertices, and let M be the distance matrix of G. We prove that if there exists w ∈ Z q such that ∑ i w i = 0 and the vector Mw, after sorting its coordinates, is an arithmetic progression with nonzero common difference, then the metric… CONTINUE READING

3 Citations

Metric Dimension, Minimal Doubly Resolving Sets, and the Strong Metric Dimension for Jellyfish Graph and Cocktail Party Graph

- Computer Science, Mathematics
- 2020

1

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 28 REFERENCES

My Brain is Open: The Mathematical Journeys of Paul Erdos.@@@The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth.

- Art, Mathematics
- 1998

111

Chv 83 ] V . Chvátal . Mastermind