Matching preclusion
In graph theory, a branch of mathematics, the matching preclusion number of a graph G {\displaystyle G} , denoted m p ( G ) {\displaystyle \mathrm {mp} (G)} , is the minimum number of edges whose deletion results in the elimination of all perfect matchings or near-perfect matchings (matchings that cover all but one vertex in a graph with an odd number of vertices). Matching preclusion measures the quality of a graph as a communications network topology for distributed algorithms that require each node of the distributed system to be matched with a neighboring partner node.