Diagnosability for a family of matching composition networks

We study here the diagnosability of networks under two models of self-diagnosis: PMC model introduced by Preparata, Metze and Chien (IEEE Trans Electronic Computers 16(12):848-854 (1967)) and MM* model introduced by Sengupta and Dahbura (IEEE Trans Computers 41(11):1386-1396 (1992)) which is the variant of the comparison model (1980). The diagnosability of a network of processors is the maximum number of faulty processors that can be identified by the network itself. Lee and Hsieh (IEEE Trans Dependable Secure Comput 8(2):246-255 (2011)) considered the diagnosability of networks obtained by connecting two networks of the same order by two perfect matchings and got the lower bounds. Usually, there is a gap between the lower bound and the exact value of the diagnosability. In this paper, we completely determine the diagnosability of this family of matching composition networks.