The regular edge connectivity of regular networks

Classical connectivity is a vital metric to assess the reliability of interconnection networks, while it has defects in the defective assumption that all neighbours of one node may fail concurrently. To overcome this deficiency, many new generalizations of traditional connectivity, such as g-component (edge) connectivity, restricted (edge) connectivity, g-extra (edge) connectivity and so on, have been suggested. For any positive integer a, the a-regular edge connectivity of a connected graph G is the minimum cardinality of an edge cut, whose deletion disconnects G so that each component is a a-regular graph. In this work, we investigate the a-regular edge connectivity of some regular networks, which provides a novel idea for further exploring the reliability of networks. Finally, simulations are carried out to compare the a-regular connectivity with other types of connectivity in some regular networks. The comparison results imply that the a-regular edge connectivity has its superiority.