Distance Optimally Edge Connectedness of Arrangement Graph Based on Subgraph Fault Pattern

Large-scale multiprocessor systems or multicomputer systems based on networking have been extensively used in the big data era and social network. Fault tolerance is becoming an essential attribute in multiprocessor systems with the increase of the system scale. For any distinct vertices [Formula: see text], the local connectivity of [Formula: see text] and [Formula: see text], denoted by [Formula: see text], is the maximum number of independent [Formula: see text]-paths in system graph [Formula: see text]. The local edge connectivity of [Formula: see text], [Formula: see text], [Formula: see text], is defined similarly. For any [Formula: see text], [Formula: see text], if [Formula: see text] (or [Formula: see text], then [Formula: see text] is [Formula: see text]-distance optimally (edge) connected, where [Formula: see text] is the diameter of [Formula: see text] and [Formula: see text] is the degree of [Formula: see text]. For any integers [Formula: see text] subject to [Formula: see text], if [Formula: see text] is [Formula: see text]-distance optimally (edge) connected, then we call [Formula: see text] is [Formula: see text]-distance local optimally (edge) connected. In this work, we show that [Formula: see text] ([Formula: see text] is [Formula: see text]-arrangement graph) is [Formula: see text]-distance local optimally edge connected for [Formula: see text] and [Formula: see text].