Rv for n = 2ζ and t = 2ϖ − 1.

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.在互联网络领域中，基于距离的参数（尤其是图的划分维数（partition dimension））在化学、计算机科学等诸多领域均有广泛应用。划分维数的一类重要变体为容错分辨划分（fault-tolerant resolving partition），其在计算机科学的网络构建、优化与导航任务中至关重要。在网络场景下，容错划分可确保即便遭遇网络故障或中断，仍能维持稳定可靠的通信路径；在优化领域，该方法可助力研发能够抵御输入数据错误或变动的高效算法；在导航系统中，容错划分可在不确定且动态的环境下，为可靠的路径规划与导航服务提供支撑。本文聚焦于带弦环图（cycle with chord graphs）特定场景下的容错划分维数，探究其特性以及对提升网络系统鲁棒性与可靠性的应用价值。