### Matching preclusion for cube-connected cycles

Qiuli Li, Wai Chee Shiu, Haiyuan Yao
2015 Discrete Applied 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 cubeconnected cycles
more » ... twork \$CCC_{n}\$. By using the super-edge-connectivity of vertex-transitive graphs, the super cyclically edge-connectivity of \$CCC_{n}\$ 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 \$CCC_{n}\$ and mainly classify respective optimal solutions. Response to Reviewers 1. All minor typos were corrected according to the suggestion of two reviewers. 2. Item 2 of reviewer #1 and item 11 of reviewer #3: We added the missing figure. 3. Item 8 of reviewer #1: We revised the statement of Theorem 2.12. Abstract 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 network CCC n . By using the super-edge-connectivity of vertex-transitive graphs, the super cyclically edge-connectivity of CCC n 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 CCC n and classify respective optimal matching preclusion sets.