Network resolvability and fault tolerance in cycle-related topologies

This article examines the fault-tolerant metric dimension (FTMD) of cycle-related networks, specifically dragon and kayak paddle networks, two structurally diverse families important for sensor placement, network design, and resilience. The primary objective is to identify minimal fault-tolerant resolving sets (FTRSs) that ensure unique identification of nodes, even under vertex failures. Using combinatorial techniques and rigorous proofs, the study reveals that while the metric dimension (MD) remains constant, the FTMD varies predictably with network structure. The exact FTMD values for these network families are determined by constructing minimal FTRSs and demonstrating their optimality. These results contribute to the understanding of robust resolvability in cycle-related topologies and highlight its significance for resilient applications such as communication networks, power grids, and autonomous navigation.