Geodesic
On the metric dimensions for sets of vertices
Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 1, pp. 245-275

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Resolving sets were originally designed to locate vertices of a graph one at a time. For the purpose of locating multiple vertices of the graph simultaneously, {𝓁}-resolving sets were recently introduced. In this paper, we present new results regarding the {𝓁}-resolving sets of a graph. In addition to proving general results, we consider {2}-resolving sets in rook's graphs and connect them to block designs. We also introduce the concept of 𝓁-solid-resolving sets, which is a natural generalisation of solid-resolving sets. We prove some general bounds and characterisations for 𝓁-solid-resolving sets and show how 𝓁-solid- and {𝓁}-resolving sets are connected to each other. In the last part of the paper, we focus on the infinite graph family of flower snarks. We consider the 𝓁-solid- and {𝓁}-metric dimensions of flower snarks. In two proofs regarding flower snarks, we use a new computer-aided reduction-like approach.
Keywords: resolving set, metric dimension, resolving several objects, block design, rook's graph, flower snark 
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     title = {On the metric dimensions for sets of vertices},
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Hakanen, Anni; Junnila, Ville; Laihonen, Tero; Puertas, Maria Luz. On the metric dimensions for sets of vertices. Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 1, pp. 245-275. http://geodesic.mathdoc.fr/item/DMGT_2023_43_1_a16/