Conditional matching preclusion for hypercube-like interconnection networks

The conditional matching preclusion number of a graph with n vertices is the minimum number of edges whose deletion results in a graph without an isolated vertex that does not have a perfect matching if n is even, or an almost perfect matching if n is odd. We develop some general properties on conditional matching preclusion and then analyze the conditional matching preclusion numbers for some HL-graphs, hypercube-like interconnection networks.