Matching preclusion and conditional matching preclusion problems for the folded Petersen cube

The matching preclusion number of an even graph is the minimum number of edges whose deletion results in a graph that has no perfect matchings. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. Recently, the conditional matching preclusion number of an even graph was introduced to look for obstruction sets beyond those induced by a single vertex. It is defined to be the minimum number of edges whose deletion results in a graph with no isolated vertices   and no perfect matchings. In this paper, we study this problem for the folded Petersen cube FPQ(n,k)FPQ(n,k) via some matching preclusion and conditional matching preclusion results of the Cartesian products of graphs.