Cyclic connectivity and cyclic diagnosability of alternating group graphs

Abstract The generalizations of the connectivity and diagnosability are significant parameters to evaluate the reliability and the fault-tolerance of multiprocessor systems, and play an important role in designing and maintaining multiprocessor systems. In order to better measure the reliability of a system, some scholars proposed the cyclic connectivity and cyclic diagnosability, which request that there are at least two components containing cycles after removing the vertex set. Interconnection networks are typically used as the underlying topologies of a multiprocessor system. In particular, alternating group graphs possess many attractive properties, such as vertex transitivity, strong hierarchy, and maximal connectivity, making them excellent choices for interconnection networks in a multiprocessor system. In this paper, we determine that the cyclic connectivity of the alternating group graph is $6n-18$ for $n\ge 4$. Moreover, we establish that its cyclic diagnosability is $8n-24$ for $n>6$ under the $PMC$ model and $MM^{*}$ model, respectively.