Fault-tolerant partition resolvability of cycle with chord.

In the realm of connected networks, distance-based parameters, particularly the partition dimension of graphs, have extensive applications across various fields, including chemistry and computer science. A notable variant of the partition dimension is the fault-tolerant resolving partition, which is critical in computer science for networking, optimization, and navigation tasks. In networking, fault-tolerant partitioning ensures robust communication pathways even in the event of network failures or disruptions. In optimization, it aids in developing efficient algorithms capable of withstanding errors or changes in input data. In navigation systems, fault-tolerant partitioning supports reliable route planning and navigation services under uncertain or dynamic conditions. This paper focuses on the fault-tolerant partition dimension within the specific context of the cycle with chord graphs, exploring its properties and implications for enhancing the robustness and reliability of networked systems.