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The \emph{matching preclusion number} of a graph is the minimum number ofedges whose deletion results in a graph that has neither perfect matchings noralmost perfect matchings. As a generalization, Liu and Liu recently introducedthe concept of fractional matching preclusion number. The \emph{fractionalmatching preclusion number} of $G$ is the minimum number of edges whosedeletion leaves the resulting graph without a fractional perfect matching. The\emph{fractional strong matching preclusion number} of $G$ is the minimumnumber of vertices and edges whose deletion leaves the resulting graph withouta fractional perfect matching. In this paper, we obtain the fractional matchingpreclusion number and the fractional strong matching preclusion number forgeneralized augmented cubes. In addition, all the optimal fractional strongmatching preclusion sets of these graphs are categorized.

Fractional matching preclusion for generalized augmented cubes