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 ...

The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. This is an extension of the matching preclusion problem that was introduced by Park and Ihm. The generalized (n, k)-star graph was introduced to address scaling issues of the star graph, and it has many de...