The regular edge connectivity of regular networks

AbstractClassical 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.KEYWORDS: Interconnection networksconnectivitya-regular edge connectivityregular networks Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was partly supported by the National Natural Science Foundation of China [grant numbers 61977016, 61572010, and 62277010], Natural Science Foundation of Fujian Province, China [grant numbers 2020J01164 and 2017J01738]. This work was also partly supported by the China Scholarship Council [CSC number 202108350054].