Paired 2-disjoint path covers of balanced hypercube under the partitioned edge fault model

The n-dimensional balanced hypercube \(BH_{n}\) $B{H}_n$ serves as a crucial interconnection network in massively parallel and distributed systems since it possesses many excellent properties. In numerous parallel applications, the construction of many-to-many disjoint path cover (m-DPC) among vertices in networks plays a central role in efficient data transmission. However, the fault tolerance of interconnection networks is overwhelmingly underestimated since the possibility all of the faulty edges to be concentrated in a certain dimension is low. In this paper, we show the existence of paired 2-disjoint path cover (2-DPC) for \(BH_{n}\) $B{H}_n$ under the partitioned edge fault (PEF) model. In particular, we show that \(BH_{n}\) $B{H}_n$ is \((2^{n - 1} - 1)\) $(2^{n-1}-1)$ -partition-edge fault-tolerant paired 2-disjoint path coverable and our results achieve the exponential tolerability for edge failures, which implies that the proposed path cover capability under partitioned edge fault model is superior to other known works on traditional edge failure.