Classification of graphs with metric dimension three and fault-tolerant metric dimension four

Characterize all maximal outerplanar graphs with metric dimension 3 and fault-tolerant metric dimension 4.

Background

The paper focuses primarily on maximal outerplanar graphs with metric dimension 2 and determines the two graphs whose fault-tolerant metric dimension is 3. It does not provide a corresponding classification for maximal outerplanar graphs whose metric dimension is 3 and whose fault-tolerant metric dimension is 4.

References

Characterize all MOPs $G$ such that $\beta (G)=3$ and $\beta'(G)=4$.

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