Strong matching preclusion for k-ary n-cubes

Shiying Wang, Kai Feng, Guozhen Zhang

Abstract: The k<math><mi is="true">k</mi></math>-ary n<math><mi is="true">n</mi></math>-cube is one of the most popular interconnection networks for parallel and distributed systems. Strong matching preclusion that additionally permits more destructive vertex faults in a graph is a more extensive form of the original matching preclusion that assumes only edge faults. In this paper, we establish the strong matching preclusion number and all minimum strong matching preclusion sets for k<math><mi is="true">k</mi></math>-ary n<math><mi is="true">n</mi></math>-cubes with n≥2<math><mi is="true">n</mi><mo is="true">≥</mo><mn is="true">2</mn></math> and k≥3<math><mi is="true">k</mi><mo is="true">≥</mo><mn is="true">3</mn></math>.