On the global strong resilience of fault Hamiltonian graphs

Abstract

The global strong resilience of G with respect to having a fractional perfect matching, also called FSMP number of G, is the minimum number of edges (or resp., edges and/or vertices) whose deletion results in a graph that has 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 edges and/or vertices with |F|≤f. In this paper, we first give a sufficient condition, involving the independent number, to determine the FSMP number of (δ−2)-fault Hamiltonian graphs with minimum degree δ≥2, and then we can derive the FSMP number of some networks, which generalize some known results.