Determine general bounds for fault-tolerant metric dimension variants

Determine what general relationships hold between the fault-tolerant parameter ftxdim(G) and the underlying metric-dimension variant xdim(G) for arbitrary variants xdim(G) of metric dimension.

Background

For every metric-dimension variant considered in the paper, the authors establish the elementary lower bound ftxdim(G) > xdim(G) + 1 and derive sharper results for particular variants. They leave unresolved the broader question of what can be said uniformly for arbitrary variants, including whether further structural or quantitative bounds exist.

References

For arbitrary variants xdim(G) of metric dimension, what else can be said in general about ftxdim(G) with respect to xdim(G)?

— Fault tolerance for metric dimension and its variants  (2502.02731 - Geneson et al., 4 Feb 2025) in Section 9, Conclusion