1-Good-Neighbor r-Component Edge-Connectivity of Augmented Cube

Widespread application of parallel and distributed systems in high-performance computing or big data processing has prompted an urgent demand for qualitative and quantitative metrics to evaluate the fault tolerability and vulnerability of underlying interconnection networks for multiprocessor systems. The 1-good-neighbor [Formula: see text]-component edge-connectivity is defined as the minimum number of edges whose removal disconnects the network into at least [Formula: see text] connected components, with each vertex holding at least one good neighbor. This paper elaborates on the 1-good-neighbor [Formula: see text]-component edge-connectivity of the augmented cube [Formula: see text], denoted as [Formula: see text]. In detail, for specific ranges of [Formula: see text] and [Formula: see text], we determine the [Formula: see text], which provides a refined quantitative basis for analyzing the robustness of multiprocessor systems under link failure scenarios.