Department of Mathematics
Matching preclusion is a measure of robustness in the event of edge failure in interconnection networks. The matching preclusion number of a graph 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 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 networkCCCn. By using the super-edge-connectivity of vertex-transitive graphs, the super cyclically edge-connectivity of CCCn for n=3,4 and 5, Hall’s Theorem and the strengthened Tutte’s Theorem, we obtain the matching preclusion number and the conditional matching preclusion number of CCCn and classify respective optimal matching preclusion sets.
Discrete Applied Mathematics
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Matching preclusion, Networks, Cube-connected cycles, Cyclically edge-connectivity
Liu, Qiuli, Wai Chee Shiu, and Haiyuan Yao. "Matching preclusion for cube-connected cycles." Discrete Applied Mathematics 190-191 (2015): 118-126.