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The conditional fractional matching preclusion number (CFMP number for short) Formula: see text of a graph Formula: see text is the minimum number of edges whose deletion results in a graph without isolated vertices and without fractional perfect matchings. In this paper, we study the CFMP number of complete graphs, complete bipartite graphs and twisted cubes. Also, we give Nordhaus–Gaddum-type results for the CFMP numbers of general graphs.
Li et al. (Tue,) studied this question.