Geodesic
Fractional matching preclusion for generalized augmented cubes
Discrete mathematics & theoretical computer science, Tome 21 (2019) no. 4.

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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. 
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     author = {Ma, Tianlong and Mao, Yaping and Cheng, Eddie and Melekian, Christopher},
     title = {Fractional matching preclusion for generalized augmented cubes},
     journal = {Discrete mathematics & theoretical computer science},
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     number = {4},
     year = {2019},
     doi = {10.23638/DMTCS-21-4-6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-4-6/}
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Ma, Tianlong; Mao, Yaping; Cheng, Eddie; Melekian, Christopher. Fractional matching preclusion for generalized augmented cubes. Discrete mathematics & theoretical computer science, Tome 21 (2019) no. 4. doi : 10.23638/DMTCS-21-4-6. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-4-6/

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