Fractional matching preclusion for generalized augmented cubes

Abstract

The \emph{matching preclusion number} of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. As a generalization, Liu and Liu recently introduced the concept of fractional matching preclusion number. The \emph{fractional matching preclusion number} of $G$ is the minimum number of edges whose deletion leaves the resulting graph without a fractional perfect matching. The \emph{fractional strong matching preclusion number} of $G$ is the minimum number of vertices and edges whose deletion leaves the resulting graph without a fractional perfect matching. In this paper, we obtain the fractional matching preclusion number and the fractional strong matching preclusion number for generalized augmented cubes. In addition, all the optimal fractional strong matching preclusion sets of these graphs are categorized.