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Some binary products and integer linear programming for k-metric dimension of graphs

Author

Listed:
  • Klavžar, Sandi
  • Rahbarnia, Freydoon
  • Tavakoli, Mostafa

Abstract

A sharp upper bound and a closed formula for the k-metric dimension of the hierarchical product of graphs is proved. Also, sharp lower bounds for the k-metric dimension of the splice and link products of graphs are presented. An integer linear programming model for computing the k-metric dimension as well as a k-metric basis of a given graph is proposed. These results are applied to bound or to compute the k-metric dimension of some classes of graphs that are of interest in mathematical chemistry.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:409:y:2021:i:c:s0096300321005099
    DOI: 10.1016/j.amc.2021.126420
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    References listed on IDEAS

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    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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