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Computing the k-metric dimension of graphs

Author

Listed:
  • Yero, Ismael G.
  • Estrada-Moreno, Alejandro
  • Rodríguez-Velázquez, Juan A.

Abstract

Given a connected graph G=(V,E), a set S ⊆ V is a k-metric generator for G if for any two different vertices u, v ∈ V, there exist at least k vertices w1,…,wk∈S such that dG(u, wi) ≠ dG(v, wi) for every i∈{1,…,k}. A metric generator of minimum cardinality is called a k-metric basis and its cardinality the k-metric dimension of G. We make a study concerning the complexity of some k-metric dimension problems. For instance, we show that the problem of computing the k-metric dimension of graphs is NP-hard. However, the problem is solved in linear time for the particular case of trees.

Suggested Citation

  • Yero, Ismael G. & Estrada-Moreno, Alejandro & Rodríguez-Velázquez, Juan A., 2017. "Computing the k-metric dimension of graphs," Applied Mathematics and Computation, Elsevier, vol. 300(C), pages 60-69.
    • Handle: RePEc:eee:apmaco:v:300:y:2017:i:c:p:60-69
    DOI: 10.1016/j.amc.2016.12.005
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    References listed on IDEAS

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    1. András Sebő & Eric Tannier, 2004. "On Metric Generators of Graphs," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 383-393, May.
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    Cited by:

    1. Kelenc, Aleksander & Kuziak, Dorota & Taranenko, Andrej & G. Yero, Ismael, 2017. "Mixed metric dimension of graphs," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 429-438.
    2. Klavžar, Sandi & Rahbarnia, Freydoon & Tavakoli, Mostafa, 2021. "Some binary products and integer linear programming for k-metric dimension of graphs," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    3. Alejandro Estrada-Moreno, 2021. "The k -Metric Dimension of a Unicyclic Graph," Mathematics, MDPI, vol. 9(21), pages 1-14, November.

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