Some binary products and integer linear programming for k-metric dimension of graphs - Klavžar, Sandi; Rahbarnia, Freydoon; Tavakoli, Mostafa (Applied mathematics and computation, 2021)
•k-metric dimension is an invariant in graphs which is difficult to compute and frequently arise in applications.•In this paper k-metric dimension of graphs is studied under some graph operations which are in turn suitable tools to approach NP-hard graph problems.•Also, an integer linear programming model for computing the k-metric dimension as well as a k-metric basis of a given graph is proposed. 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.