Swapped optical transpose interconnection system: Fault-tolerant resolvability on cycle graphs

Within computing and information technology, interconnection systems are often modeled using graphs. A notable example is the swapped Optical Transpose Interconnection System (OTIS). Ensuring resilience to faults is crucial in optoelectronic systems. Across different fault classifications that can arise in an interconnection structure, two notable ones are the failure of a node (such as a processor in the case of OTIS over base graph G, denoted by OG and the disruption in facilitating communication between nodes breakdown of processor-to-processor communication). To manage these faults, it is crucial to assign a unique identifier to each node. In terms of graph theory, this corresponds to identifying the metric dimension, denoted as β(G), and Fault-oriented metric dimension β′(G) of the graph G representing the interlinking structure. This paper analyzes the OTIS architecture based on Cm (Cycle graph containing m vertices), represented as OCm, for resolvability and resolvability under fault conditions. It is proved that β(OCm)=m−1 and β′(OCm)=m.