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}
}
  • Zilin Jiang, N. Polyanskii
  • Published 2019
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. A
  • 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

    Figures and Topics from this paper.

    Maker-Breaker resolving game
    The Query Complexity of Mastermind with lp Distances

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 28 REFERENCES