Fractional matching preclusion of fault Hamiltonian graphs

Matching preclusion is a measure of robustness in the event of edge failure in interconnection networks. As a generalization of matching preclusion, the fractional matching preclusion number (FMP number for short) of a graph is the minimum number of edges whose deletion results in a graph that has no fractional perfect matchings, and the fractional strong matching preclusion number (FSMP number for short) of a graph is the minimum number of edges and/or vertices whose deletion leaves a resulting graph with no fractional perfect matchings. A graph $G$ is said to be $f$-fault Hamiltonian if there exists a Hamiltonian cycle in $G-F$ for any set $F$ of vertices and/or edges with $|F|\leq f$. In this paper, we establish the FMP number and FSMP number of $(\delta-2)$-fault Hamiltonian graphs with minimum degree $\delta\geq 3$. As applications, the FMP number and FSMP number of some well-known networks are determined.