The cyclic diagnosability of Cayley graphs generated by transposition trees

Abstract

The system’s self diagnosis capability is a critical indicator for the reliability of multiprocessor systems, which plays a key role in ensuring the smooth operation of big data processing and cloud computing. Cycle structures, which bring redundant paths for secure communication, enhance network reliability significantly. Based on cyclic connectivity, cyclic diagnosability has been proposed and has witnessed a small amount of progress. Although the metric relationship between cyclic connectivity and cyclic diagnosability has been established, the flexibility of generating graph of Cayley graphs prevents this metric relationship from being directly applied to characterize the cyclic diagnosability of all Cayley graphs generated by transposition trees. In this paper, we classify the generating transposition trees based on the diameter and the number of matchings, and determine the cyclic diagnosability of Cayley graphs generated by these transposition trees under PMC and MM* models.