The metric dimension, also known as the resolvability, of a graph is a fundamental concept in graph theory that measures the smallest number of vertices (called resolving set) required to uniquely identify each vertex in the graph. Research in the metric dimension of graphs is an active area of study, and several interesting problems have been investigated. While I cannot provide you with the absolute top-rated problems as research is constantly evolving, I can mention some important and well-studied problems in this field:

These are just a few examples of research problems in the metric dimension (resolvability) of graphs. The field is vast, and there are numerous other interesting questions and directions that researchers continue to explore.

Some recent interesting variations are multiset dimension (see Simanjuntak et al.), local multiset dimension, non-local multiset dimension and outer multiset dimension (see Klavzar et al.) All of these are based on the idea of resolving vertices based on the multiset of distances without associating the distances with specific landmarks. An article that came out this week is 'resolving vertices of graphs with differences'.