Computational complexity of fault-tolerant metric dimension

Determine whether computing the fault-tolerant metric dimension of a maximal outerplanar graph is NP-hard.

Background

The paper establishes structural results for the fault-tolerant metric dimension of maximal outerplanar graphs, including exact classifications for graphs with fault-tolerant metric dimension 3 and bounds for graphs of metric dimension 2. It does not resolve the computational complexity of determining this parameter for an input maximal outerplanar graph. The stated problem asks for either an NP-hardness proof or a disproof of NP-hardness.

References

Given a MOP $G$, prove or disprove whether computing the FTMD of $G$ is NP-hard.

— On the fault-tolerant metric dimension of maximal outerplanar graphs  (2610.13374 - Hernando et al., 9 Oct 2026) in Section Conclusions, first Open problem