Fault tolerance assessment for half-vertex transitive networks based on 3-extra edge fault pattern

Fault tolerance is an important criterion for assessing the reliability of multiprocessor systems, and connectivity is a specific parameter. As an extension of traditional edge-connectivity, t-extra edge-connectivity is an essential parameter for evaluating the fault tolerance of interconnection networks. A half-vertex transitive network is a type of double-orbit network with at most two vertex orbits. In this paper, we determine the exact value of 3-extra edge-connectivity and characterize the 3-extra edge-cut for half-vertex transitive networks. In addition, the obtained results can be applied to both general and well-known network classes, including the Bi-Cayley networks.