The processors within a multiprocessor system use an interconnection network for communication and data transmission, hence the structure of the interconnection network determines various aspects of the system’s performance. In the event of processor failures within the system, the system’s fault diagnosis capability is very significant. Diagnosability is the crucial parameter for evaluating the fault diagnosis capability of the interconnection network in multiprocessor systems. Studying diagnosability using diagnosis model such as the PMC model is beneficial for improving and optimizing multiprocessor systems. This paper uses the lexicographic product to generate a network structure \(P_m \circ K_{x,y}\) which helps maintain the system’s parallel processing capability and high-performance computing. When \(m \ge 4\) , \(x+y \ge 5\) and \(y>x\) , the diagnosability of \(P_m \circ K_{x,y}\) under the PMC model is found to be \(2x+y\) , and when \(0 \le h<2x+y\) , its h-edge fault tolerance diagnosability is \(2x+y-h\) .