The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. Park and Ihm introduced the problem of strong matching preclusion under the condition that no isolated vertex is created as a result of faults. In this paper, we find the conditional strong matching preclusion number for the $n$-dimensional alternating group graph $AG_n$.
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Abdallah, Mohamad and Cheng, Eddie
"Conditional Strong Matching Preclusion of the Alternating Group Graph,"
Theory and Applications of Graphs: Vol. 6
, Article 5.
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol6/iss2/5