Matching preclusion for vertex-transitive networks

In interconnection networks, matching preclusion is a measure of robustness when there is a link failure. Let G be a graph of even order. The matching preclusion number mp(G) is defined as the minimum number of edges whose deletion results in a subgraph without perfect matchings. Many interconnection networks are super matched, that is, their optimal matching preclusion sets are precisely those induced by a single vertex. In this paper, we obtain general results of vertextransitive graphs including many known networks. A k-regular connected vertex-transitive graph has matching preclusion number k and is super matched except for six classes of graphs. From this many previous results can be directly obtained and matching preclusion for some other networks, such as folded k-cubes, Hamming graphs and halved k-cubes, are derived.