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

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... 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|≤ f. In this paper, we establish the FMP number and FSMP number of (δ-2)-fault Hamiltonian graphs with minimum degree δ≥ 3. As applications, the FMP number and FSMP number of some well-known networks are determined.