ON THE METRIC DIMENSIONS FOR SETS OF VERTICES 1

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 si-multaneously, {t} -resolving sets were recently introduced. In this paper, we present new results regarding the {t} -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 t -solid-resolving sets, which is a natural generalisation of solid-resolving sets. We prove some general bounds and characterisations for t-solid-resolving sets and show how t -solid-and {t} -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 t -solid-and {t} -metric dimensions of flower snarks. In two proofs regarding flower snarks, we use a new computer-aided reduction-like approach.