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A note on the complexity of k-metric dimension

Author

Listed:
  • Schmitz, Yannick
  • Vietz, Duygu
  • Wanke, Egon

Abstract

Two vertices u,v∈V of an undirected connected graph G=(V,E) are resolved by a vertex w if the distance between u and w and the distance between v and w are different. A set R⊆V of vertices is a k-resolving set for G if for each pair of vertices u,v∈V there are at least k distinct vertices w1,…,wk∈R such that each of them resolves u and v. The k-Metric Dimension of G is equal to the size of a smallest k-resolving set for G. The decision problem k-Metric Dimension is the question whether G has a k-resolving set of size at most r, for a given graph G and a given number r. In this paper, we proof the NP-completeness of k-Metric Dimension for bipartite graphs and each k≥2, which corrects the proof in [1].

Suggested Citation

  • Schmitz, Yannick & Vietz, Duygu & Wanke, Egon, 2023. "A note on the complexity of k-metric dimension," Applied Mathematics and Computation, Elsevier, vol. 457(C).
    • Handle: RePEc:eee:apmaco:v:457:y:2023:i:c:s0096300323003739
    DOI: 10.1016/j.amc.2023.128204
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