Fractional matching preclusion of fault Hamiltonian graphs [article]

Huiqing Liu, Shunzhe Zhang, Xinyuan Zhang
2020 arXiv   pre-print
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
more » ... 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.
arXiv:2001.03713v2 fatcat:xu2sreae7reppeq63foj3zxjkq