The strong matching preclusion is a measure for the robustness of interconnection networks in the presence of node and/or link failures. However, in the case of random link and/or node failures, it is unlikely to find all the faults incident and/or adjacent to the same vertex. This motivates Park et al. to introduce the conditional strong matching preclusion of a graph. In this paper we consider the conditional strong matching preclusion problem of the augmented cube $AQ_n$, which is a variation of the hypercube $Q_n$ that possesses favorable properties.
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Abdallah, Mohamad and Cheng, Eddie
"The Conditional Strong Matching Preclusion of Augmented Cubes,"
Theory and Applications of Graphs: Vol. 8
, Article 5.
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol8/iss1/5