Authors: Kratica, Jozef 
Kovačević-Vujčić, Vera
Čangalović, Mirjana
Stojanović, Milica
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Minimal doubly resolving sets and the strong metric dimension of some convex polytopes
Journal: Applied Mathematics and Computation
Volume: 218
Issue: 19
First page: 9790
Last page: 9801
Issue Date: 1-Jun-2012
Rank: M21
ISSN: 0096-3003
DOI: 10.1016/j.amc.2012.03.047
In this paper we consider two similar optimization problems on graphs: the strong metric dimension problem and the problem of determining minimal doubly resolving sets. We prove some properties of strong resolving sets and give an integer linear programming formulation of the strong metric dimension problem. These results are used to derive explicit expressions in terms of the dimension n, for the strong metric dimension of two classes of convex polytopes Dn and Tn. On the other hand, we prove that minimal doubly resolving sets of Dn and Tn have constant cardinality for n>7.
Keywords: Convex polytopes | Minimal doubly resolving set | Strong metric dimension
Publisher: Elsevier
Project: Graph theory and mathematical programming with applications in chemistry and computer science 

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