Matching preclusion for cube-connected cycles ?
Matching preclusion is a measure of robustness in the event of edge failure in interconnection networks. The matching preclusion number of a graph G G with even order is the minimum number of edges whose deletion results in a graph without perfect matchings and the conditional matching preclusion number of G G is the minimum number of edges whose deletion leaves the resulting graph with no isolated vertices and without perfect matchings. We consider matching preclusion of cube-connected cycles network CCCn C C C n . By using the super-edge-connectivity of vertex-transitive graphs, the super cyclically edge-connectivity of CCCn C C C n for n=3,4 n = 3 , 4 and 5, Halls Theorem and the strengthened Tuttes Theorem, we obtain the matching preclusion number and the conditional matching preclusion number of CCCn C C C n and classify respective optimal matching preclusion sets.
matching preclusion cube-connected cycles networks cyclically edge-connectivity