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

Sandi Klavžar, Freydoon Rahbarnia and Mostafa Tavakoli

Applied Mathematics and Computation, 2021, vol. 409, issue C

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.

Keywords: Metric dimension; k-metric dimension; Binary product; Integer linear programming; Chemical graph theory (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:409:y:2021:i:c:s0096300321005099

DOI: 10.1016/j.amc.2021.126420

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