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The k -Metric Dimension of a Unicyclic Graph

Author

Listed:
  • Alejandro Estrada-Moreno

    (Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Av. Països Catalans 26, 43007 Tarragona, Spain)

Abstract

Given a connected graph G = ( V ( G ) , E ( G ) ) , a set S ⊆ V ( G ) is said to be a k -metric generator for G if any pair of different vertices in V ( G ) is distinguished by at least k elements of S . A metric generator of minimum cardinality among all k -metric generators is called a k -metric basis and its cardinality is the k -metric dimension of G . We initially present a linear programming problem that describes the problem of finding the k -metric dimension and a k -metric basis of a graph G . Then we conducted a study on the k-metric dimension of a unicyclic graph.

Suggested Citation

  • Alejandro Estrada-Moreno, 2021. "The k -Metric Dimension of a Unicyclic Graph," Mathematics, MDPI, vol. 9(21), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2789-:d:671425
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    References listed on IDEAS

    as
    1. Ron Adar & Leah Epstein, 2017. "The k-metric dimension," Journal of Combinatorial Optimization, Springer, vol. 34(1), pages 1-30, July.
    2. 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.
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