The matching preclusion number of a graph, introduced in [2] as a fault analysis, is the minimum number of edges whose deletion leaves a resulting graph that has neither perfect matchings nor almost perfect matchings. As a generalization, Liu and Liu [14] recently introduced the concept of fractional matching preclusion number. The fractional matching preclusion number of graph is the minimum number of edges whose deletion results in a graph that has no fractional perfect matching. If the sets of edges of the graph attaining the minimum are precisely those incident to a single vertex of minimum degree, we say such graph is fractional super matched. In this paper, the upper and lower bounds for the fractional matching preclusion number for Cartesian product, direct product, strong product, and lexicographic product are obtained, and we give sufficient conditions for such graphs to be fractional super matched.

图[2]中作为故障分析引入的图的匹配排除数是其删除留下的结果图既没有完美匹配也几乎没有完美匹配的边的最小数量。作为概括，Liu和Liu [14]最近引入了分数匹配排除数的概念。图的分数匹配排除数是其删除导致图中没有分数完美匹配的边的最小数量。如果图的达到最小的边集恰好是入射到最小度的单个顶点的边，那么我们说这种图是分数超匹配的。本文获得了笛卡尔乘积，直接乘积，强乘积和字典序乘积的分数匹配排除数的上限和下限，并且我们为此类图提供了分数超匹配的充分条件。