  The strong matching preclusion number of a graph, introduced by Park and Ihm
in 2011, is the minimum number of vertices and edges whose deletion results in
a graph that has neither perfect matchings nor almost perfect matchings. As a
generalization, the fractional strong matching preclusion number of a graph is
the minimum number of edges and vertices whose deletion leaves the resulting
graph without a fractional perfect matching. In this paper, we obtain the
fractional strong matching preclusion number for Cartesian product graphs. As
an application, the fractional strong matching preclusion number for torus
networks is obtained.
