Reliability and conditional diagnosability of hyper bijective connection networks

The g-extra connectivity and diagonalisability are two important metrics to fault-tolerance and robustness of a multiprocessor system whose network structure is modelled by a graph. In this work, we explore the reliability of a newly proposed network called hyper bijective connection networks (HBC, for short), which is an extension of the family of the well-known interconnection networks, such as hypercube and its variants. We prove that 2-extra vertex connectivity and 3-extra vertex connectivity of n-dimensional HBC are 3n + m−6 for and and 4n + m−8 for and , respectively. Using its desirable fault-tolerance, we show that the conditional diagonalizabilities of n-dimensional HBC under the PMC model are m + 4n−7 (resp., 4n−5) for and (resp., m = 3 and ) and its conditional diagonalizability under MM model is m + 3n−6 for and .