Fractional matching preclusion of graphs

Let F be an edge subset and $F^{\prime }$ a subset of edges and vertices of a graph G. If $G‐F$ and $G‐F^{\prime }$ have no fractional perfect matchings, then F is a fractional matching preclusion (FMP) set and $F^{\prime }$ is a fractional strong MP (FSMP) set of G. The FMP (FSMP) number of G is the minimum size of FMP (FSMP) sets of G. In this paper, the FMP number and the FSMP number of Petersen graph, complete graphs and twisted cubes are obtained, respectively.