Fault-Tolerant Resolvability of Swapped Optical Transpose Interconnection System

Abstract

Interconnection systems in computer science and information technology are mainly represented by graphs. One such instance is of swapped network simulated by the optical transpose interconnection system (OTIS). Fault tolerance has become a vital feature of optoelectronic systems. Among multiple types of faults that may take place in an interconnection system, two significant kinds are either due to malfunctioning of a node (processor in case of $O_G$ ) or collapse of communication between nodes (failure of interprocessor transmission). To prevail over these faults, the unique recognition of every node is essential. In graph-theoretic interpretation, this leads to instigating the metric dimension $\beta \left(O_G\right)$ and fault-metric dimension $\beta {}^{\prime }\left(O_G\right)$ of the graph $O_G$ obtained from the interconnection system. This paper explores OTIS over base graph $P_m$ (path graph over m vertices) for resolvability and fault-tolerant resolvability. Furthermore, bounds for $\beta \left(O_G\right)$ and $\beta \prime \left(O_G\right)$ are also imparted over $G=P_m$ .